title: Running Man (South Korean TV series)

text: "Running Man" was originally classified as an "urban action variety"; a genre of variety shows in an urban environment. The MCs and guests were to complete missions at a landmark to win the race. The show has since shifted to a more familiar reality-variety show concept focused on games. It has garnered attention as being the comeback program for Yoo Jae-suk, the main MC of the program, after leaving "Good Sunday"s "Family Outing" in February 2010.


title: Running Man (South Korean TV series)

text: The show has become popular in other parts of Asia, and has gained online popularity among Hallyu fans, having been fansubbed into various languages, such as English, Persian, Spanish, Portuguese, French, Italian, Thai, Vietnamese, Chinese, Malay, Indonesian, Burmese, Arabic, Russian, and Turkish.


title: Running Man (South Korean TV series)

text: Since April 2017, "Running Man" is airing as the first part of "Good Sunday" at 4:50 pm KST and competing against KBS2's "The Return of Superman" and MBC's "King of Mask Singer". "Running Man" previously aired at 6:25 pm KST on Sundays, as the second part of "Good Sunday", competing against KBS2's "2 Days & 1 Night". The show had its special episode on Sunday, July 12, 2020, in celebration of their 10th anniversary.


title: Running Man (South Korean TV series)

text: As of episode 48, the members have taken part in a series of missions to become the winner(s) at the end of the race. Missions form the basis of "Running Man" as members try to avoid punishment in earlier episodes or to win prizes. Multiple missions are presented in each episode, with the highlight of "Running Man" being "race missions". The format of the show has veered away from the "race mission + others" to "one continuous race + missions".


title: Running Man (South Korean TV series)

text: The original cast members consists of Yoo Jae-suk, Gary, Haha, Ji Suk-jin, Kim Jong-kook, Lee Kwang-soo and Song Joong-ki. Song Ji-hyo was originally a guest for the second (episode 2–3) and third landmark (episode 4–5). She officially joined the program in the fourth landmark (episode 6) but was unable to attend until the fifth landmark (episode 7). In April 2011, Song Joong-ki recorded his last episode (episode 41) in May, and has left the program to focus on his acting career but returned on episode 66 as a guest after leaving for almost half a year, and later made cameo appearances in several episodes. After School's Lizzy was initially a guest for episode 13 and 14, and would later join in episode 18 as official member. However, she left show from episode 26 due to schedule conflicts with her group activities. She later returned as a guest in episode 292, 5 years since her last appearance. On October 25, 2016, Gary announced his departure from the show to focus on his music career after being with "Running Man" for 6 years, but later returned as a guest, a week after his final recording. On April 3, 2017, it was confirmed through various media outlets that "Running Man" is adding actress Jeon So-min and comedian Yang Se-chan. On April 27, 2021, Lee Kwang-soo announced his departure, becoming the third original cast member to leave the show.


title: Running Man (South Korean TV series)

text: The staff run the games, often showing up on camera either by actively participating in the game or influencing the outcome of various missions.


title: Running Man (South Korean TV series)

text: This includes the personal cameramen (VJs), production directors (PDs), floor directors (FDs), stylists, boom operators, etc.


title: Running Man (South Korean TV series)

text: Chief producer, Nam Seung-yong, is responsible for the production of the program, with PD Jo Hyo-jin, Im Hyung-taek, and Kim Joo-hyung (also known as Myeok PD) mainly responsible for the directing and production of the recordings of the program since inception. Other PDs have joined the program to assist as the program shifts from a single landmark to multiple locations for recording, notably Hwang Seon-man, Jeong Cheol-min, and Lee Hwan-jin. FD Go Dong-wan assists in the recordings of the program and is known to be shown on camera many times, as well as delivering and assisting the members in missions. Producer Kim Joo-hyung has left the show as of episode 182 as he was reassigned to "Inkigayo".


title: Running Man (South Korean TV series)

text: Each member has their own personal cameramen who follow them around exclusively during recordings. Notable cameramen include Ryu Kwon-ryeol (Yoo Jae-suk's primary VJ), Kim Yoo-seok (Jee Seok-jin's primary VJ), Choi Yoon-sang (former primary VJ for Lee Kwang-soo), Yoon Sung-yong (Haha's primary VJ), Sung Gyu (Song Ji-hyo's primary VJ), Jo Seong-Oh (Gary's primary VJ, now Yang Se-chan's primary VJ), Kim Ki-jin (Kim Jong-kook's primary VJ), and Ji Bong-jo (Jeon So-min's primary VJ).


title: Running Man (South Korean TV series)

text: On November 19, 2014, the show's head director, Jo Hyo-jin, announced his departure from the show after working with the members for four years.


title: Running Man (South Korean TV series)

text: On March 20, 2016, the show's main PD, Im Hyung-taek left the show (as of episode 291) as he became the producer of "Hurry Up, Brother", resulting in new generation PDs to take over, notably PD Lee Hwan-jin, PD Jeong Cheol-min, and PD Park Yong-woo. FD Go Dong-wan also announced his leave via his Instagram.


title: Running Man (South Korean TV series)

text: On July 3, 2016, SBS confirmed the return of producer Kim Joo-hyung to the show. That same month, it is confirmed that he will be the new main PD of the show. However, it didn't last long as PD Kim Joo-hyung announced that he is leaving the show shortly after. Subsequently, PD Lee Hwan-jin took over as the main PD of "Running Man" until March 2017. In April 2017, PD Jeong Cheol-min took over from PD Lee Hwan-Jin as the "Running Man" main PD.


title: Running Man (South Korean TV series)

text: In July 2018, PD Jeong Cheol-min took a break and PD Lee Hwan-jin temporarily took over as main PD of the show. PD Jeong returned in May 2019 replacing PD Lee, leading the show till February 5, 2020, where he left the show and SBS. His role was taken over by PD Choi Bo-pil.


title: Running Man (South Korean TV series)

text: On August 1, 2022, SBS announced that PD Choi Bo-pil would be leaving the show, with PD Choi Hyung-in taking over the role, making her the first female production director in the show's history.


title: Running Man (South Korean TV series)

text: During its run, some of the guests were occasionally featured or invited to the show. The following list are guests who appeared the most often as of November 27, 2022.


title: Running Man (South Korean TV series)

text: Many guests have taken part in "Running Man". The following is a compilation of guests and the number of times they have been on the show.


title: Running Man (South Korean TV series)

text: With regards to guest-turned-members (Song Ji-hyo, Jeon So-min, Yang Se-chan) or former members of the show (Lizzy, Song Joong-ki, Gary, Lee Kwang-soo ), only the times they were a guest are counted. The guests were sorted according to their appearances and the number of episodes appeared.


title: Running Man (South Korean TV series)

text: The first episode of the show received mixed reviews. According to "Asiae", the show concept was promising, but the crew could not use the location to full potential, and the pace was not fast and dynamic enough.


title: Running Man (South Korean TV series)

text: Despite a slow start, "Running Man" became increasingly popular in South Korea and throughout Asia. In its home country the show is watched by 2.1 million people on average. Due to the existence of fansubs, it is watched outside of Asia as well, being translated into English, Spanish and Arabic, among others.


title: Running Man (South Korean TV series)

text: According to "The Straits Times" (an English language daily newspaper in Singapore), the popularity of the show is due to its unpredictability, the comedy involved, the celebrity guests and the chemistry between the regular cast members. Assistant professor Liew Kai Khiun at the Nanyang Technological University (Singapore) attributes the appeal of "Running Man" to the ability of using public space in a creative way: "Running Man is about taking audiences to the various corners of not only South Korea, but the region as well. In the rather fast-paced urban societies in Asia, the show helps to provide release from the daily tensions that such streets and buildings are associated with." Liew thinks that the cast members are not particularly good looking, thus have nothing to lose, even if they "wrestle with one another like children".


title: Running Man (South Korean TV series)

text: According to producer Jo Hyo-jin, the show is popular because the concept of having to choose a winner is culturally easy to understand. He also named the good relationship between the regular members as one of the reasons for the show's success. Celebrity guests like Super Junior, Girls' Generation and f(x) play an important part in the success as well, although they sometimes induce criticism. For example, after the airing of the Big Bang episodes, some viewers complained that the band won too easily. Jo Hyo-jin, however, denied any special treatment of the celebrities. Jo explained that fans are also highly critical of the games, therefore it is not possible for the crew to reuse games without changing them.


title: Running Man (South Korean TV series)

text: The regular members of "Running Man" have held several fan meetings throughout Asia. In October 2013, their Singapore fan meeting drew a crowd of 3,000. When the cast arrived for shooting in Vietnam and other countries, they were greeted by thousands of fans at the airport.


title: Running Man (South Korean TV series)

text: In conjunction with the 9th year of show, the show held their first ever fan-meeting in South Korea. During the fan-meeting, they collaborate with the different singers. On September 22, 2019, the extended play titled "Running Man Fan Meeting: Project Running 9" was released.


title: Running Man (South Korean TV series)

text: In the ratings below, the highest rating for the show is in , and the lowest rating for the show is in each year.


title: Running Man (South Korean TV series)

text: In order to "relay the feeling of "Running Man"", "Running Man" has made merchandises available on sale since 2015. The products ranging from stickers, socks, hats, shirts, and shoes.


title: Running Man (South Korean TV series)

text: On May 26, 2015, a special project called the ""Running Man" Challenge" was made in collaboration with a footwear co-created platform, ROOY. Its main objective is for the fans to design a shoe that "would unify and coordinate between the cast members." 777 submissions were made, and in June 2015, a design made by a fan named Noh Seung-soo was selected to be the official design for the shoes. The shoes went on sale on February 22, 2016. Currently, a second ""Running Man" Challenge" is held. The winner for this challenge will have their design to be the new shoes.


title: Running Man (South Korean TV series)

text: On June 14, 2017, it was announced that "Running Man" will be adapted into a half-hour animated show. It features the original seven members, including former member Gary, in animal form. The show will have 24 episodes and EXO-CBX will provide the theme song for it. Additionally, the animated show will be the first to be broadcast in UHD in South Korea. On August 11, 2018, the animated show premiered on Cartoon Network in Southeast Asia as an English dub.


title: Running Man (South Korean TV series)

text: On December 5, 2018, the "Running Man, 2018" animated series was released in theaters. On December 19, 2020, an animated movie, originally serving as a six-episode preview of the new season, premiered on Cartoon Network in Southeast Asia as an English dub with the title "Running Man: The Ultimate Challenge".


title: Running Man (South Korean TV series)

text: In March 2013, a comic book adaptation of the series was published. The series, titled "Running Man: How do I Find the Kidnapped Idol?", is written by Hong Yong-hoon and illustrated by Kim Moon-shik. The comic book, which is aimed for children, was released on March 25, 2013.


title: Running Man (South Korean TV series)

text: On March 30 and 31, 2019, a play which was titled, "The Musical Running Man" was performed at Busan Citizen's Hall.


title: Running Man (South Korean TV series)

text: Running Man had first sold the franchise to China which became "Running Man China" in 2014. They later sold the franchise to Vietnam and Indonesia in 2019.


title: Running Man (South Korean TV series)

text: "Outrun by Running Man" is the first official spin-off series of the long running programmme, featuring original cast members Haha, Jee Seok-jin and Kim Jong-kook. The show premiered on November 12, 2021, and is available for streaming on Disney+ platform.


title: Running Man (South Korean TV series)

text: In September 2012, Gary made a surprising announcement on social media about his intention to leave the program. It is believed that his intention came from the recent criticism concerning the "Super 7 Concert" which his company, Leessang Company, was producing. Gary decided to take responsibility for its failure by resigning himself from any activities. Due to this, "Running Man" production staff and the members decided to postpone their filming schedule on September 24–25, 2012 to convince him to stay in the program. A week later, Gary officially apologized for the controversy he created and confirmed his decision to remain as a member of the program. In 2016, Gary again announced his departure from Running Man to focus on his music. This caused Running Man to have a 6-member cast for a few months before casting two new members, Yang Se Chan and Jeon So Min. Gary returned on episode 336 as a surprise guest.


title: Running Man (South Korean TV series)

text: On December 14, 2016, it was announced that Kim Jong-kook and Song Ji-hyo were leaving the show, as a new season with a new format starring the remaining cast members and new member Kang Ho-dong would air in January 2017. Initial reception was mixed. However, it was revealed that Kim Jong-kook and Song Ji-hyo were not given any notice about their removal, resulting in an overwhelming negative reaction. In addition, news of Kang refusing the offer to join the new season resulted in a possible cancellation of Season 2 of "Running Man".


title: Running Man (South Korean TV series)

text: On December 16, 2016, an emergency meeting was held with the consensus reached that all members would leave, ending the program altogether in February 2017 with a subsequent program taking its place.


title: Running Man (South Korean TV series)

text: However, on January 24, 2017, SBS announced that the show will continue airing with all of the remaining cast members. The decision came after Nam Seung-yong, the new Vice President of SBS Entertainment Headquarters, who was involved in conceiving "Running Man", had further conversations with every member in regards to the show's future. Subsequently, after apologizing to Kim Jong-kook and Song Ji-hyo for all of the issues regarding the program, the former then became actively involved in convincing the other members to continue working on the program.


title: Running Man (South Korean TV series)

text: On April 28, 2019, Running Man was criticized for plagiarizing Naver webtoon “Money Game”. The aired episode showed cast members put into a studio and given money to spend as a group. The fans of the "Money Game" webtoon pointed out the similarities between the episode concept and the webtoon's storyline. “Money Game” writer Bae Jin-Soo and Naver Webtoon, the platform in which the webtoon is published, both stated that they never received prior notificafion or requests for consent to be able to adopt the "Money Game" storyline into a Running Man episode. In response, producers of Running Man issued an apology to both parties.


title: Running Man (South Korean TV series)

text: During an episode aired on December 7, 2020, the show depicted China and Taiwan as separate countries when playing a board game, which caused outrage and call for boycotts in China.


title: Molly Ringwald

text: Molly Kathleen Ringwald (born February 18, 1968) is an American actress, singer, dancer, and author. She was cast in her first major role as Molly in the NBC sitcom "The Facts of Life" (1979–80) after a casting director saw her playing an orphan in a stage production of the musical "Annie". She and several other members of the original "Facts of Life" cast were let go when the show was reworked by the network. She subsequently made her motion-picture debut as Miranda in the independent film "Tempest" (1982), which earned her a Golden Globe nomination for New Star of the Year.


title: Molly Ringwald

text: Ringwald is known for her collaborations with filmmaker John Hughes. She established herself as a teen icon after appearing in the successful Hughes films "Sixteen Candles" (1984), "The Breakfast Club" (1985), and "Pretty in Pink" (1986). She later starred in "The Pick-up Artist" (1987), "Fresh Horses" (1988), and "For Keeps" (1988). She starred in many films in the 1990s, most notably "" (1992), "The Stand" (1994), and "Some Folks Call It a Sling Blade" (1994 short film – precursor to "Sling Blade").


title: Molly Ringwald

text: Ringwald was part of the "Brat Pack" and she was ranked number one on VH1's 100 Greatest Teen Stars. Since 2017, Ringwald has portrayed Mary Andrews on The CW television series "Riverdale".


title: Molly Ringwald

text: Ringwald was born in Roseville, California, the daughter of Adele Edith ("née" Frembd), a chef, and Robert Scott "Bob" Ringwald, a blind jazz pianist of German descent. Ringwald has two siblings, Beth and Kelly, and an older brother, who died before she was born. She is partly of Swedish descent. She started her acting career at age five, appearing in a stage production of "Alice in Wonderland" as the Dormouse. The next year, she recorded "I Wanna Be Loved by You", a music album of Dixieland jazz with her father and his group, the Fulton Street Jazz Band. Ringwald graduated from the Lycée Français de Los Angeles.


title: Molly Ringwald

text: In 1978 at the age of 10, Ringwald was chosen to play Kate in the West Coast production of "Annie", performing in Los Angeles. In 1979, Ringwald appeared on the TV series "Diff'rent Strokes" and was selected to become part of the large cast of that show's spin-off, "The Facts of Life". She played Molly Parker, a perky, feminist student at Eastland Girls School. At the beginning of the second season, the show underwent a major revamp, and most of the cast, including Ringwald, were cut from the show. Ringwald later said that Nancy McKeon replaced her to play a new character named Jo.


title: Molly Ringwald

text: In 1980, Ringwald performed as a lead vocalist on two Disney albums. On the patriotic album "Yankee Doodle Mickey", Ringwald sang "This Is My Country", "The Star-Spangled Banner", and "God Bless America". She later performed one track, "The First Noel", on a Disney Christmas album, "Disney’s Christmas All-Time Favorites". Turning toward motion pictures, she got a key supporting role in the 1982 film "Tempest", directed by Paul Mazursky with top casting director Juliet Taylor, and was nominated for a Golden Globe award for the role.


title: Molly Ringwald

text: Ringwald rose to prominence with her breakout role in "Sixteen Candles" (1984). She was cast as Samantha Baker, a girl whose sixteenth birthday is forgotten by her family. Ringwald's performance gained critical acclaim; many called her acting engaging. Ringwald would later say, "It is not a good idea to do remakes of great classic films" when asked if there would be a remake to "Sixteen Candles".


title: Molly Ringwald

text: Ringwald was regarded as a member of the Brat Pack of 1980s teen actors but has said she was not really part of that group.


title: Molly Ringwald

text: Ringwald gained more success when she was cast in another John Hughes film, "The Breakfast Club" (1985), which was a commercial and critical success. Ringwald was cast as Claire Standish, a spoiled, wealthy beauty who is in detention for skipping class to go to the mall. Ringwald's performance gained strong reviews.


title: Molly Ringwald

text: The following year, still in high school, she was cast as Andie Walsh in another successful Hughes film, "Pretty In Pink" (1986). When first asked to be in "Pretty in Pink", Ringwald was reluctant, but after seeing how hard it was for the producers to find a replacement for her, she decided she would portray Andie in the film. Ringwald was offered a role in another John Hughes film, "Some Kind of Wonderful" (1987), but turned down the role as she felt it was too similar to the other films she worked on with Hughes. After "Pretty In Pink", she wanted to act in more mature roles. Ringwald was featured on the cover of the May 26, 1986, issue of "Time".


title: Molly Ringwald

text: Ringwald was set to star in another Hughes film, "Oil and Vinegar", but the film was scrapped when Hughes refused to rewrite the script. The film would have been about a soon-to-be-married man and a hitchhiking girl talking about their lives during the length of a car ride. In 1987, she was cast as Randy Jensen in "The Pick-up Artist", opposite Robert Downey, Jr. in one of his first lead roles. It focused on a womanizer who meets his match when he falls for a woman in debt to the Mafia. The film was met with mixed reviews while being a moderate commercial success.


title: Molly Ringwald

text: The following year, she starred in "For Keeps," a commercial success that received mixed reviews from critics but was well received by audiences. It is considered Ringwald's final teen movie. Ringwald portrayed Darcy Elliot, the editor at her high school paper, who becomes pregnant by her long-term boyfriend Stan, portrayed by Randall Batinkoff. Her performance received positive reviews. The film was praised by some critics for showing the struggles of teen pregnancy. She was later cast in "Fresh Horses". The film was met with generally negative reviews and underperformed at the box office. The film also starred Andrew McCarthy, who previously worked with Ringwald in "Pretty in Pink".


title: Molly Ringwald

text: In the early 1990s, Ringwald reportedly turned down the female lead roles in "Pretty Woman" and "Ghost". In the mid-1990s, Ringwald, who had been educated at the Lycée Français de Los Angeles and is fluent in French, moved to Paris and starred in several French movies. She returned to the United States intermittently to appear in American movies and television. In 1990, Ringwald appeared in the James Scott-directed "Strike It Rich" alongside Robert Lindsay and John Gielgud. That same year she starred in "Betsy's Wedding" as Betsy Hopper. This film gained generally mixed reviews despite being a commercial success. Ringwald later starred in "" (1992).


title: Molly Ringwald

text: In 1994, she was cast as Frannie Goldsmith in the TV miniseries "The Stand", an adaptation of Stephen King's 1978 novel of the same name. Ringwald's performance was generally well received. She next played the leading role in the film "Malicious" (1995) as Melissa Nelson, a disturbed woman who has an affair with a college star baseball player. She later starred in the ABC sitcom "Townies". She appeared as a blind woman on the critically acclaimed cable series "Remember WENN". She starred with Lara Flynn Boyle and Teri Hatcher in the 1998 made-for-television film "Since You've Been Gone". In 1999, she played the starring role of "Li'l Bit" in Paula Vogel's play "How I Learned to Drive" at the Mark Taper Forum in Los Angeles. In 2000, she appeared in an episode of Showtime's "The Outer Limits", "Judgment Day".


title: Molly Ringwald

text: In 2000, Ringwald appeared in the ensemble restaurant-themed film "In the Weeds", and in 2001 she had a cameo in the commercially successful "Not Another Teen Movie" that earned her a MTV Movie Award nomination. In theater, she wore a "Green, Green Dress" in Jonathan Larson's Off-Broadway musical "tick, tick... BOOM!", and headlined as Sally Bowles in Broadway's long-running revival of "Cabaret" from December 18, 2001, until April 28, 2002. In 2003, Ringwald appeared in "Enchanted April" on Broadway beginning April 8, but left after the performance of June 15 due to her pregnancy with her daughter.


title: Molly Ringwald

text: In late 2004, she starred in the play "Modern Orthodox" on Broadway, opposite Jason Biggs and Craig Bierko. In 2006 she starred in the television film "The Wives He Forgot", and that fall and winter starred as Charity Hope Valentine in the national tour of the Broadway revival of the musical "Sweet Charity". She also played a supporting role as Molly McIntire's mother Helen in "". Ringwald starred in the ABC Family network's series "The Secret Life of the American Teenager", which debuted on July 1, 2008, and ran for five seasons and 121 episodes, before ending on June 3, 2013. She played Anne Juergens, the title teenager's mother.


title: Molly Ringwald

text: Ringwald read the audiobook edition of the 2012 novel "The Middlesteins" by Jami Attenberg. In early 2013, Ringwald released "Except Sometimes", a jazz record. It follows a tradition in jazz for the Ringwald family set by her father. "I grew up in a home filled with music and had an early appreciation of jazz since my dad was a jazz musician. Beginning at around age three I started singing with his band and jazz music has continued to be one of my three passions along with acting and writing. I like to say jazz music is my musical equivalent of comfort food. It's always where I go back to when I want to feel grounded," Ringwald said in a statement.


title: Molly Ringwald

text: Ringwald played Madame Frechette in the 2014 Lifetime Christmas film "Wishin' and Hopin'". Ringwald plays Aunt Bailey in "Jem and the Holograms", raising Jerrica, her sister Kimber, and adopted daughters. In September 2014, Ringwald began writing an advice column for "The Guardian", answering questions about "love, family, or life in general". In 2016, she was cast as Amy in the crime-drama film "King Cobra". Ringwald currently has a recurring role as main character Archie Andrews' mother Mary Andrews on The CW television series "Riverdale". After initially only appearing as a guest, Ringwald has taken a more prominent role in the series following the death of Luke Perry who played Archie's father.


title: Molly Ringwald

text: In 2019 Ringwald made her debut as a translator, providing the English translation of the French novel "Lie With Me" by Philippe Besson.


title: Molly Ringwald

text: Ringwald married Valéry Lameignère, a French writer, in Bordeaux, France, on July 28, 1999; they divorced in 2002. She married Panio Gianopoulos, a Greek-American writer and book editor, in 2007. They have a daughter, born in 2003 and fraternal boy-girl twins, born in July 2009. Her pregnancy was written into the storyline of "The Secret Life of the American Teenager". She was the subject of an episode in season 7 of the genealogy series "Who Do You Think You Are?".


title: Molly Ringwald

text: Ringwald has stated that she was very aware of her public image during her teen years and that she tried to be a good role model for her fans. When asked about "For Keeps" (1988), Ringwald said, "I didn't want to give the wrong message to teenagers. I sort of felt a certain responsibility – I mean, I was a very, very famous teenager and I thought a lot of teenagers were looking up to me and emulating me, and I really didn't want to make a movie that said in any way that having a baby at that age was going to be easy."


title: Bigfoot

text: Bigfoot, also commonly referred to as Sasquatch, is a purported ape-like creature said to inhabit the forest of North America. Many dubious articles have been offered in attempts to prove the existence of Bigfoot, including anecdotal claims of sightings as well as alleged video and audio recordings, photographs, and casts of large footprints. Some are known or admitted hoaxes. Tales of wild, hairy humanoids exist throughout the world, and such creatures appear in the folklore of North America, including the mythologies of indigenous people. Bigfoot is an icon within the fringe subculture of cryptozoology, and an enduring element of popular culture.


title: Bigfoot

text: The majority of mainstream scientists have historically discounted the existence of Bigfoot, considering it to be the result of a combination of folklore, misidentification, and hoax, rather than a living animal. Folklorists trace the phenomenon of Bigfoot to a combination of factors and sources including indigenous cultures, the European wild man figure, and folk tales. Wishful thinking, a cultural increase in environmental concerns, and overall societal awareness of the subject have been cited as additional factors.


title: Bigfoot

text: Other creatures of relatively similar descriptions are alleged to inhabit various regions throughout the world, such as the Skunk ape of the southeastern United States; the Almas, Yeren, and Yeti in Asia; and the Australian Yowie; all of which, like Bigfoot, are engrained in the cultures of their regions.


title: Bigfoot

text: Bigfoot is most often described as a large, muscular, and bipedal ape-like creature covered in black, dark brown, or dark reddish hair. Anecdotal descriptions estimate a height of roughly , with some descriptions having the creatures standing as tall as . Some alleged observations describe Bigfoot as more "man-like", with reports of a human-like face. In 1971, multiple people in The Dalles, Oregon, filed a police report describing an "overgrown ape", and one of the men claimed to have sighted the creature in the scope of his rifle, but could not bring himself to shoot it because, "It looked more human than animal".


title: Bigfoot

text: Common descriptions also include broad shoulders, no visible neck, and long arms, which skeptics describe as likely misidentification of a bear standing upright. Some alleged nighttime sightings have stated the creature's eyes "glowed" yellow or red. However, eyeshine is not present in humans or any other known apes and so proposed explanations for observable eyeshine off of the ground in the forest include owls, raccoons, or opossums perched in foliage.


title: Bigfoot

text: Michael Rugg, owner of the Bigfoot Discovery Museum in Northern California, claims to have smelled Bigfoot, stating, "Imagine a skunk that had rolled around in dead animals and had hung around the garbage pits".


title: Bigfoot

text: The enormous footprints for which the creature is named are claimed to be as large as long and wide. Some footprint casts have also contained claw marks, making it likely that they came from known animals such as bears, which have five toes and claws.


title: Bigfoot

text: Many of the indigenous cultures across the North American continent include tales of mysterious hair-covered creatures living in forests, and according to anthropologist David Daegling, these legends existed long before contemporary reports of "Bigfoot". These stories differed in their details both regionally and between families in the same community.


title: Bigfoot

text: On the Tule River Indian Reservation in Central California, petroglyphs created by a tribe of Yokuts at a site called Painted Rock are alleged by some to depict a group of Bigfoot called "the Family". The local tribespeople call the largest of the glyphs "Hairy Man" and they are estimated to be between 500 and 1000 years old. 16th century Spanish explorers and Mexican settlers in California told tales of the "los Vigilantes Oscuros", or "Dark Watchers", large creatures alleged to stalk their camps at night. In the region that is now Mississippi, a French Jesuit priest was living with the Natchez in 1721 and reported stories of hairy creatures in the forest known to scream loudly and steal livestock.


title: Bigfoot

text: Ecologist Robert Pyle argues that most cultures have accounts of human-like giants in their folk history, expressing a need for "some larger-than-life creature". Each language had its own name for the creature featured in the local version of such legends. Many names mean something along the lines of "wild man" or "hairy man", although other names describe common actions that it was said to perform, such as eating clams or shaking trees. Chief Mischelle of the Nlaka'pamux at Lytton, British Columbia told such a story to Charles Hill-Tout in 1898.


title: Bigfoot

text: The Sts'ailes people tell stories about "sasq'ets", a shapeshifting creature that protects the forest. The name "Sasquatch" is the anglicized version of "sasq'ets" (sas-kets), roughly translating to "hairy man" in the Halq'emeylem language.


title: Bigfoot

text: Members of the Lummi tell tales about creatures known as "Ts'emekwes". The stories are similar to each other in the general descriptions of "Ts'emekwes", but details differed among various family accounts concerning the creature's diet and activities. Some regional versions tell of more threatening creatures: the "stiyaha" or "kwi-kwiyai" were a nocturnal race, and children were warned against saying the names so that the "monsters" would not come and carry them off to be killed. The Iroquois tell of an aggressive, hair covered giant with rock-hard skin known as the "Ot ne yar heh" or "Stone Giant", more commonly referred to as the "Genoskwa". In 1847, Paul Kane reported stories by the natives about "skoocooms", a race of cannibalistic wild men living on the peak of Mount St. Helens in southern Washington state. Also related to this area was an alleged incident in 1924 in which a violent encounter between a group of gold prospectors and a group of "ape-men" occurred. These allegations were reported in the July 16, 1924, issue of "The Oregonian" and have become a popular piece of Bigfoot lore, with the area now being referred to as Ape Canyon. U.S. President Theodore Roosevelt, in his 1893 book, "The Wilderness Hunter", writes of a story he was told by an elderly mountain man named Bauman in which a foul smelling, bipedal creature ransacked his beaver trapping camp, stalked him, and later became hostile when it fatally broke his companion's neck in the wilderness near the Idaho-Montana border. Roosevelt notes that Bauman appeared fearful while telling the story, but attributed the trapper's folkloric German ancestry to have potentially influenced him.


title: Bigfoot

text: Less-menacing versions have also been recorded, such as one by Reverend Elkanah Walker from 1840. Walker was a Protestant missionary who recorded stories of giants among the natives living near Spokane, Washington. These giants were said to live on and around the peaks of the nearby mountains, stealing salmon from the fishermen's nets.


title: Bigfoot

text: In 1958, Jerry Crew, a logging company bulldozer operator in Humboldt County, California, discovered a set of large, human-like footprints sunk deep within the mud in the Six Rivers National Forest. Upon informing his coworkers, many claimed to have seen similar tracks on previous job sites as well as telling of odd incidents such as an oil drum weighing having been moved without explanation. The logging company men soon began utilizing the term "Bigfoot" to describe the mysterious culprit. Crew, who initially believed someone was playing a prank on them, once again observed more of these numerous, massive footprints and contacted reporter Andrew Genzoli of the "Humboldt Times" newspaper. Genzoli interviewed lumber workers and wrote articles about the mysterious footprints, introducing the name "Bigfoot" in relation to the tracks and the local tales of large, hairy wild men. A plaster cast was made of the footprints and Crew appeared, holding one of the casts, on the front page of the newspaper on October 6, 1958. The story spread rapidly as Genzoli began to receive correspondence from major media outlets including the "New York Times" and "Los Angeles Times". As a result, the term "Bigfoot" became widespread as a reference to an apparently large, unknown creature leaving massive footprints in Northern California.


title: Bigfoot

text: In 2002, the family of Crew's deceased coworker Ray Wallace stated that their father had been secretly making the large footprints with carved, wooden feet and that he was responsible for the tracks. Despite the Wallace family's statement, Willow Creek and Humboldt County are considered by some to be the "Bigfoot Capital of the World".


title: Bigfoot

text: In the 1830s, a Wyandot chief was nicknamed "Big Foot" due to his significant size, strength and large feet. Potawatomi Chief Maumksuck, known as Chief "Big Foot", is today synonymous with the area of Walworth County, Wisconsin and has a state park and school named for him. William A. A. Wallace, a famous 19th century Texas Ranger, was nicknamed "Bigfoot" due to his large feet and today has a town named for him: Bigfoot, Texas. Lakota leader Spotted Elk was also called "Chief Big Foot". In the late 19th and early 20th centuries, at least two enormous marauding grizzly bears were widely noted in the press and each nicknamed "Bigfoot". The first grizzly bear called "Bigfoot" was reportedly killed near Fresno, California in 1895 after killing sheep for 15 years; his weight was estimated at 2,000 pounds (900 kg). The second one was active in Idaho in the 1890s and 1900s between the Snake and Salmon rivers, and supernatural powers were attributed to it.


title: Bigfoot

text: According to "Live Science", there have been over 10,000 reported Bigfoot sightings in the continental United States. About one-third of all claims of Bigfoot sightings are located in the Pacific Northwest, with the remaining reports spread throughout the rest of North America. Most reports are considered mistakes or hoaxes, even by those researchers who claim Bigfoot exists.


title: Bigfoot

text: Sightings predominantly occur in the northwestern region of Washington, Oregon, Northern California, and British Columbia. Other prominent areas of supposed sightings include the rural areas of the Great Lakes region and the southeastern United States. According to data collected from the Bigfoot Field Researchers Organization's (BFRO) Bigfoot sightings database in 2019, Washington has over 2,000 reported sightings, California over 1,600, Pennsylvania over 1,300, New York and Oregon over 1,000, and Texas has just over 800. The debate over the legitimacy of Bigfoot sightings reached a peak in the 1970s, and Bigfoot has been regarded as the first widely popularized example of pseudoscience in American culture.


title: Bigfoot

text: Many regions have differentiating names for the creatures. In Canada, the name "Sasquatch" is widely used although often interchangeably with the name "Bigfoot". The United States uses both of these names but also has numerous names and descriptions of the creatures depending on the region and area in which they are allegedly sighted. These include the "Skunk ape" in Florida and other southern states, "Grassman" in Ohio, "Fouke Monster" in Arkansas, "Wood Booger" in Virginia, the "Monster of Whitehall" in Whitehall, New York, "Momo" in Missouri, "Honey Island Swamp Monster" in Louisiana, "Dewey Lake Monster" in Michigan, "Mogollon Monster" in Arizona, the "Big Muddy Monster" in southern Illinois, and "The Old Men of the Mountain" in West Virginia. The term "Wood Ape" is also used by some as a means to deviate from the perceived mythical connotation surrounding the name "Bigfoot". Other names include "Bushman", "Treeman", and "Wildman".


title: Bigfoot

text: Some Bigfoot researchers allege that Bigfoot throws rocks as territorial displays and for communication. Other alleged behaviors include audible blows struck against trees or "wood knocking", further alleged to be communicative.


title: Bigfoot

text: Additionally, structures of broken and twisted foliage seemingly placed in specific areas have been attributed by some to Bigfoot behavior. In some reports, lodgepole pine and other small trees have been observed bent, uprooted, or stacked in patterns such as weaved and crisscrossed, leading some to theorize that they are potential territorial markings. Some instances have also included entire deer skeletons being suspended high in trees. In Washington state, a team of amateur Bigfoot researchers called the Olympic Project claimed to have discovered a collection of nests, and they had primatologists study them, with the conclusion being that they appear to have been created by a primate.


title: Bigfoot

text: Many alleged sightings are reported to occur at night leading to some speculations that the creatures may possess nocturnal tendencies. However, experts find such behavior untenable in a supposed ape- or human-like creature, as all known apes, including humans, are diurnal, with only lesser primates exhibiting nocturnality. Most anecdotal sightings of Bigfoot describe the creatures allegedly observed as solitary, although some reports have described groups being allegedly observed together.


title: Bigfoot

text: Alleged vocalizations such as howls, screams, moans, grunts, whistles, and even a form of supposed language have been reported and allegedly recorded. Some of these alleged vocalization recordings have been analyzed by individuals such as retired U.S. Navy cryptologic linguist Scott Nelson. He analyzed audio recordings from the early 1970s said to be recorded in the Sierra Nevada mountains dubbed the "Sierra Sounds" and stated, "It is definitely a language, it is definitely not human in origin, and it could not have been faked". Les Stroud has spoken of a strange vocalization he heard in the wilderness while filming "Survivorman" that he stated sounded primate in origin. The majority of mainstream scientists maintain that the source of the sounds often attributed to Bigfoot are either hoaxes, anthropomorphization, or likely misidentified and produced by known animals such as owl, wolf, coyote, and fox.


title: Bigfoot

text: A story from 1924, often referred to as the "Battle of Ape Canyon", presents miners being attacked by large, hairy "ape men" that threw rocks onto their cabin roof from a nearby cliff after one of the miners allegedly shot one with a rifle. In Fouke, Arkansas in 1971, a family reported that a large, hair-covered creature startled a woman after reaching through a window. This alleged incident was later deemed a hoax.


title: Bigfoot

text: In 1974, the "New York Times" presented the dubious tale of Albert Ostman, a Canadian prospector, who stated that he was kidnapped and held captive by a family of Bigfoot for six days in 1924 in Toba Inlet, British Columbia.


title: Bigfoot

text: The 2021 Hulu documentary series, "Sasquatch", describes marijuana farmers telling stories of Bigfoots harassing and killing people within the Emerald Triangle region in the 1970s through the 1990s; and specifically the alleged murder of three migrant workers in 1993. Investigative journalist David Holthouse attributes the stories to illegal drug operations using the local Bigfoot lore to scare away competition, specifically superstitious immigrants, and that the high rate of murder and missing persons in the area is attributed to human actions.


title: Bigfoot

text: There have also been reports of dogs allegedly being killed by a Bigfoot. In the early 1990s, 9-1-1 audio recordings were made public in which a homeowner in Kitsap County, Washington called law enforcement for assistance with a large subject, described by him as being "all in black", having entered his backyard. He previously reported to law enforcement that his dog was killed recently when it was thrown over his fence. Anthropologist Jeffrey Meldrum notes that any large predatory animal is potentially dangerous to humans, specifically if provoked, but indicates that most anecdotal accounts of Bigfoot encounters result in the creatures hiding or fleeing from people. Some amateur researchers have reported the creatures moving or taking possession of intentional "gifts" left by humans such as food and jewelry, and leaving items in their place such as rocks and twigs. Skeptics argue that many of these alleged human interactions are easily hoaxed, the result of misidentification, or are outright fabrications.


title: Bigfoot

text: Various explanations have been suggested for sightings and to offer conjecture on what existing animal has been misidentified in supposed sightings of Bigfoot. Scientists typically attribute sightings either to hoaxes or to misidentification of known animals and their tracks, particularly black bears.


title: Bigfoot

text: Mainstream scientists theorize that American black bears are a likely culprit for most Bigfoot sightings, particularly when observers view a subject from afar, are in dense foliage or there are poor lighting conditions. Additionally, black bears have been observed and recorded walking upright, often as the result of an injury. While upright, adult black bears stand roughly , and grizzly bears roughly , both within the range of anecdotal Bigfoot reports.


title: Bigfoot

text: In 2007, the Bigfoot Field Researchers Organization put forward photos which they stated showed a juvenile Bigfoot. The Pennsylvania Game Commission, however, stated that the photos were of a bear with mange. The Pennsylvania Game Commission unsuccessfully attempted to locate the suspected mangey bear. Scientist Vanessa Woods, after estimating that the subject in the photo had approximately long arms and a torso, concluded it was more comparable to a chimpanzee.


title: Bigfoot

text: Some have proposed that sightings of Bigfoot may simply be people observing and misidentifying known great apes such as chimpanzees, gorillas, and orangutans that have escaped from captivity such as zoos, circuses, and exotic pets belonging to private owners. This explanation is often proposed in relation to the Bigfoot-like Skunk ape, as some argue the humid subtropical climate of the southeastern United States could potentially support a population of escaped apes.


title: Bigfoot

text: Humans have been mistaken for Bigfoot, with some incidents leading to injuries. In 2013, a 21-year-old man in Oklahoma was arrested after he told law enforcement he accidentally shot his friend in the back while their group was allegedly hunting for Bigfoot. In 2017, a shamanist wearing clothing made of animal furs was vacationing in a North Carolina forest when local reports of alleged Bigfoot sightings flooded in. The Greenville Police Department issued a public notice not to shoot Bigfoot in fear of someone in a fur suit mistakenly being injured or killed. In 2018, a person was shot at multiple times by a hunter near Helena, Montana who claimed he mistook him for a Bigfoot.


title: Bigfoot

text: Additionally, some have attributed feral humans or hermits living in the wilderness as being another explanation for alleged Bigfoot sightings. One famous story, the Wild Man of the Navidad, tells of a wild ape-man who roamed the wilderness of eastern Texas in the mid-19th century, stealing food and goods from local residents. A search party allegedly captured an escaped African slave who was attributed to the story. During the 1980s, a number of psychologically damaged American Vietnam veterans were stated by the state of Washington's veterans' affairs director, Randy Fisher, to have been living in remote wooded areas of the state.


title: Bigfoot

text: Some have proposed that pareidolia may explain Bigfoot sightings, specifically the tendency to observe human-like faces and figures within the natural environment. Photos and videos of poor quality alleged to depict Bigfoots are often attributed to this phenomenon and commonly referred to as "Blobsquatch".


title: Bigfoot

text: Both Bigfoot believers and non-believers agree that many of the reported sightings are hoaxes or misidentified animals. Author Jerome Clark argues that the Jacko Affair was a hoax, involving an 1884 newspaper report of an ape-like creature captured in British Columbia. He cites research by John Green, who found that several contemporaneous British Columbia newspapers regarded the alleged capture as highly dubious, and notes that the "Mainland Guardian" of New Westminster, British Columbia wrote, "Absurdity is written on the face of it."


title: Bigfoot

text: In 1968, the frozen corpse of a supposed hair covered hominid measuring was paraded around the United States as part of a traveling exhibition. Many stories surfaced as to its origin such as it having been killed by hunters in Minnesota or killed by American soldiers near Da Nang during the Vietnam War. It was attributed by some to be proof of Bigfoot-like creatures. Primatologist John R. Napier studied the subject and concluded it was a hoax made of latex. Others disputed this, claiming Napier did not study the original subject. As of 2013, the subject, dubbed the Minnesota Iceman, is on display at the "Museum of the Weird" in Austin, Texas.


title: Bigfoot

text: Tom Biscardi, long-time Bigfoot enthusiast and CEO of "Searching for Bigfoot, Inc.", appeared on the "Coast to Coast AM" paranormal radio show on July 14, 2005, and said that he was "98% sure that his group will be able to capture a Bigfoot which they had been tracking in the Happy Camp, California area." A month later, he announced on the same radio show that he had access to a captured Bigfoot and was arranging a pay-per-view event for people to see it. He appeared on "Coast to Coast AM" again a few days later to announce that there was no captive Bigfoot. He blamed an unnamed woman for misleading him, and said that the show's audience was gullible.


title: Bigfoot

text: On July 9, 2008, Rick Dyer and Matthew Whitton posted a video to YouTube, claiming that they had discovered the body of a dead Bigfoot in a forest in northern Georgia. Tom Biscardi was contacted to investigate. Dyer and Whitton received $50,000 from "Searching for Bigfoot, Inc." The story was covered by many major news networks, including BBC, CNN, ABC News, and Fox News. Soon after a press conference, the alleged Bigfoot body was delivered in a block of ice in a freezer with the Searching for Bigfoot team. When the contents were thawed, observers found that the hair was not real, the head was hollow, and the feet were rubber. Dyer and Whitton admitted that it was a hoax after being confronted by Steve Kulls, executive director of SquatchDetective.com.


title: Bigfoot

text: In August 2012, a man in Montana was killed by a car while perpetrating a Bigfoot hoax using a ghillie suit.


title: Bigfoot

text: In January 2014, Rick Dyer, perpetrator of a previous Bigfoot hoax, said that he had killed a Bigfoot in September 2012 outside San Antonio. He claimed to have had scientific tests conducted on the body, "from DNA tests to 3D optical scans to body scans. It is the real deal. It's Bigfoot, and Bigfoot's here, and I shot it, and now I'm proving it to the world." He said that he had kept the body in a hidden location, and he intended to take it on tour across North America in 2014. He released photos of the body and a video showing a few individuals' reactions to seeing it, but never released any of the tests or scans. He refused to disclose the test results or to provide biological samples. He said that the DNA results were done by an undisclosed lab and could not be matched to identify any known animal. Dyer said that he would reveal the body and tests on February 9, 2014, at a news conference at Washington University, but he never made the test results available. After the Phoenix tour, the Bigfoot body was taken to Houston.


title: Bigfoot

text: On March 28, 2014, Dyer admitted on his Facebook page that his "Bigfoot corpse" was another hoax. He had paid Chris Russel of "Twisted Toybox" to manufacture the prop from latex, foam, and camel hair, which he nicknamed "Hank". Dyer earned approximately US$60,000 from the tour of this second fake Bigfoot corpse. He stated that he did kill a Bigfoot, but did not take the real body on tour for fear that it would be stolen.


title: Bigfoot

text: In April 2022, a man in Mobile, Alabama posted photos he claimed were of a Bigfoot to his Facebook page, indicating the Mobile County Sheriff's Office validated their authenticity and the team from "Finding Bigfoot" was being dispatched. The photos circulated on social media, attracting the attention of NBC 15. The man admitted the photos were an April Fools' Day hoax.


title: Bigfoot

text: On July 7, 2022, wildlife educator and media personality Coyote Peterson released a post on Facebook in which he claimed to have discovered a large primate skull in British Columbia, indicating that he had excavated and smuggled the skull into the United States for primatologist review. He further claimed to have initially hidden the discovery due to concerns that government agencies may intervene. The post went viral, quickly garnering the attention of multiple scientists who dismissed the skull as likely a replica of a gorilla skull. Darren Naish, a vertebrate paleontologist, stated, "I'm told that Coyote Peterson does this sort of thing fairly often as clickbait, and that this is a stunt done to promote an upcoming video. Maybe this is meant to be taken as harmless fun. But in an age where anti-scientific feelings and conspiracy culture are a serious problem it—again—really isn't a good look. I think this stunt has backfired".


title: Bigfoot

text: Bigfoot proponents Grover Krantz and Geoffrey H. Bourne both believed that Bigfoot could be a relict population of the extinct southeast Asian ape species "Gigantopithecus blacki". According to Bourne, "G. blacki" may have followed the many other species of animals that migrated across the Bering land bridge to the Americas. To date, no "Gigantopithecus" fossils have been found in the Americas. In Asia, the only recovered fossils have been of mandibles and teeth, leaving uncertainty about "G. blacki"s locomotion. Krantz has argued that "G. blacki" could have been bipedal, based on his extrapolation from the shape of its mandible. However, the relevant part of the mandible is not present in any fossils. The more popular view is that "G. blacki" was quadrupedal, as its enormous mass would have made it difficult for it to adopt a bipedal gait.


title: Bigfoot

text: The trouble with this account is that "Gigantopithecus" was not a hominin and maybe not even a crown group hominoid; yet the physical evidence implies that Bigfoot is an upright biped with buttocks and a long, stout, permanently adducted hallux. These are hominin autapomorphies, not found in other mammals or other bipeds. It seems unlikely that "Gigantopithecus" would have evolved these uniquely hominin traits in parallel.


title: Bigfoot

text: Bernard G. Campbell writes: "That "Gigantopithecus" is in fact extinct has been questioned by those who believe it survives as the Yeti of the Himalayas and the Sasquatch of the north-west American coast. But the evidence for these creatures is not convincing."


title: Bigfoot

text: Primatologist John R. Napier and anthropologist Gordon Strasenburg have suggested a species of "Paranthropus" as a possible candidate for Bigfoot's identity, such as "Paranthropus robustus", with its gorilla-like crested skull and bipedal gait —despite the fact that fossils of "Paranthropus" are found only in Africa.


title: Bigfoot

text: Michael Rugg of the Bigfoot Discovery Museum presented a comparison between human, "Gigantopithecus," and "Meganthropus" skulls (reconstructions made by Grover Krantz) in episodes 131 and 132 of the Bigfoot Discovery Museum Show. Bigfoot enthusiasts that think Bigfoot may be the "missing link" between apes and humans have promoted the idea that Bigfoot is a descendent of "Gigantopithecus blacki", but that ape diverged from orangutans around 12 million years ago and is not related to humans.


title: Bigfoot

text: Some suggest Neanderthal, "Homo erectus", or "Homo heidelbergensis" to be the creature, but, like all other great apes, no remains of any of those species have been found in the Americas.


title: Bigfoot

text: Expert consensus is that allegations of the existence of Bigfoot are not credible science. Belief in the existence of such a large, ape-like creature is more often attributed to hoaxes, confusion, or delusion rather than to sightings of a genuine creature. In a 1996 "USA Today" article, Washington State zoologist John Crane said, "There is no such thing as Bigfoot. No data other than material that's clearly been fabricated has ever been presented."


title: Bigfoot

text: As with other similar beings, climate and food supply issues would make such a creature's survival in reported habitats unlikely. Bigfoot is alleged to live in regions unusual for a large, nonhuman primate, i.e., temperate latitudes in the northern hemisphere; all recognized nonhuman apes are found in the tropics of Africa and Asia. Great apes have not been found in the fossil record in the Americas, and no Bigfoot remains are known to have been found. Phillips Stevens, a cultural anthropologist at the University at Buffalo, summarized the scientific consensus as follows:


title: Bigfoot

text: In the 1970s, when Bigfoot "experts" were frequently given high-profile media coverage, McLeod writes that the scientific community generally avoided lending credence to such fringe theories by refusing even to debate them.


title: Bigfoot

text: Primatologist Jane Goodall was asked for her personal opinion of Bigfoot in a 2002 interview on National Public Radio's "Science Friday". She joked, "Well, now you will be amazed when I tell you that I'm sure that they exist."


title: Bigfoot

text: She later added, chuckling, "Well, I'm a romantic, so I always wanted them to exist", and finally, "You know, why isn't there a body? I can't answer that, and maybe they don't exist, but I want them to." In 2012, when asked again by the "Huffington Post", Goodall said "I'm fascinated and would actually love them to exist," adding, "Of course, it's strange that there has never been a single authentic hide or hair of the Bigfoot, but I've read all the accounts."


title: Bigfoot

text: Paleontologist and author Darren Naish states in a 2016 article for "Scientific American" that if "Bigfoot" existed, an abundance of evidence would also exist that cannot be found anywhere today, making the existence of such a creature exceedingly unlikely.


title: Bigfoot

text: A request to register the species name "Homo sapiens cognatus" was made by veterinarian Melba S. Ketchum, lead of The Sasquatch Genome Project, following publication of "Novel North American Hominins, Next Generation Sequencing of Three Whole Genomes and Associated Studies", Ketchum, M. S., et al., in the DeNovo: Journal of Science, 13 Feb 2013. The article examined 111 samples of blood, tissue, hair, and other specimens "characterized and hypothesized" to have been "obtained from elusive hominins in North America commonly referred to as Sasquatch."


title: Bigfoot

text: The title "DeNovo: Journal of Science" in which the paper was published was later found to be a Web site—registered only nine days before the paper was announced—whose first and only "journal" issue contained nothing but the "Sasquatch" article described above.


title: Bigfoot

text: In 2013, ZooBank, the non-governmental organization that is generally accepted by zoologists to assign species names, approved the registration request for the subspecies name "Homo sapiens cognatus" to be used for the reputed hominid more familiarly known as Bigfoot or Sasquatch. "Cognatus" is a Latin term meaning "related by blood."


title: Bigfoot

text: According to a statement by an ICZN associate scientist, "ZooBank and the ICZN do not review evidence for the legitimacy of organisms to which names are applied – that is outside our mandate, and is really the job of the relevant taxonomic/biological community (in this case, primatologists) to do that. When H. s. cognatus was first registered, needless to say we received a lot of inquiry about it. We scrutinized the original description and registration of this name as best as we could, and as far as we can determine, all the requirements were fulfilled for establishing the new name. Thus, at the moment, we have no grounds to reject the scientific name. This says nothing about the legitimacy of the taxon concept – it's just about whether the name was established according to the rules."


title: Bigfoot

text: Opinions of primatologists are generally against the existence of the purported species, as described above.


title: Bigfoot

text: Ivan T. Sanderson and Bernard Heuvelmans, founders of the subculture and pseudoscience of cryptozoology, have spent parts of their career searching for Bigfoot. Later scientists who researched the topic included Jason Jarvis, Carleton S. Coon, George Allen Agogino and William Charles Osman Hill, though they later stopped their research due to lack of evidence for the alleged creature.


title: Bigfoot

text: John Napier asserts that the scientific community's attitude towards Bigfoot stems primarily from insufficient evidence. Other scientists who have shown varying degrees of interest in the creature are Grover Krantz, Jeffrey Meldrum, John Bindernagel, David J. Daegling, George Schaller, Russell Mittermeier, Daris Swindler, Esteban Sarmiento, and Mireya Mayor.


title: Bigfoot

text: One study was conducted by John Napier and published in his book "Bigfoot: The Yeti and Sasquatch in Myth and Reality" in 1973. Napier wrote that if a conclusion is to be reached based on scant extant "'hard' evidence," science must declare "Bigfoot does not exist." However, he found it difficult to entirely reject thousands of alleged tracks, "scattered over 125,000 square miles" (325,000 km) or to dismiss all "the many hundreds" of eyewitness accounts. Napier concluded, "I am convinced that Sasquatch exists, but whether it is all it is cracked up to be is another matter altogether. There must be "something" in north-west America that needs explaining, and that something leaves man-like footprints."


title: Bigfoot

text: In 1974, the National Wildlife Federation funded a field study seeking Bigfoot evidence. No formal federation members were involved and the study made no notable discoveries. Also in 1974, the now defunct North American Wildlife Research Team constructed a "Bigfoot trap" in the Rogue River–Siskiyou National Forest in Jackson County, Oregon. It was baited with animal carcasses and captured multiple bears, but no Bigfoot. Upkeep of the trap ended in the early 1980s, but in 2006 the United States Forest Service repaired the trap, which today is a tourist destination along the Collings Mountain hiking trail.


title: Bigfoot

text: Beginning in the late 1970s, physical anthropologist Grover Krantz published several articles and four book-length treatments of Sasquatch. However, his work was found to contain multiple scientific failings including falling for hoaxes.


title: Bigfoot

text: A study published in the "Journal of Biogeography" in 2009 by J.D. Lozier et al. used ecological niche modeling on reported sightings of Bigfoot, using their locations to infer preferred ecological parameters. They found a very close match with the ecological parameters of the American black bear, "Ursus americanus". They also note that an upright bear looks much like a Bigfoot's purported appearance and consider it highly improbable that two species should have very similar ecological preferences, concluding that Bigfoot sightings are likely misidentified sightings of black bears.


title: Bigfoot

text: In the first systematic genetic analysis of 30 hair samples that were suspected to be from Bigfoot-like creatures, only one was found to be primate in origin, and that was identified as human. A joint study by the University of Oxford and Lausanne's Cantonal Museum of Zoology and published in the "Proceedings of the Royal Society B" in 2014, the team used a previously published cleaning method to remove all surface contamination and the ribosomal mitochondrial DNA 12S fragment of the sample. The sample was sequenced and then compared to GenBank to identify the species origin. The samples submitted were from different parts of the world, including the United States, Russia, the Himalayas, and Sumatra. Other than one sample of human origin, all but two are from common animals. Black and brown bears accounted for most of the samples, other animals include cow, horse, dog/wolf/coyote, sheep, goat, deer, raccoon, porcupine, and tapir. The last two samples were thought to match a fossilized genetic sample of a 40,000 year old polar bear of the Pleistocene epoch; a second test identified the hairs as being from a rare type of brown bear.


title: Bigfoot

text: In 2019, the FBI declassified an analysis it conducted on alleged Bigfoot hairs in 1976. Amateur Bigfoot researcher Peter Byrnes sent the FBI 15 hairs attached to a small skin fragment and asked if the bureau could assist him in identifying it. Jay Cochran, Jr., assistant director of the FBI's Scientific and Technical Services division responded in 1977 that the hairs were of deer family origin.


title: Bigfoot

text: After what "The Huffington Post" described as "a five-year study of purported Bigfoot (also known as Sasquatch) DNA samples", but prior to peer review of the work, DNA Diagnostics, a veterinary laboratory headed by veterinarian Melba Ketchum issued a press release on November 24, 2012, claiming that they had found proof that the Sasquatch "is a human relative that arose approximately 15,000 years ago as a hybrid cross of modern "Homo sapiens" with an unknown primate species." Ketchum called for this to be recognized officially, saying that "Government at all levels must recognize them as an indigenous people and immediately protect their human and Constitutional rights against those who would see in their physical and cultural differences a 'license' to hunt, trap, or kill them." Failing to find a scientific journal that would publish their results, Ketchum announced on February 13, 2013, that their research had been published in the "DeNovo Journal of Science". "The Huffington Post" discovered that the journal's domain had been registered anonymously only nine days before the announcement. This was the only edition of DeNovo and was listed as Volume 1, Issue 1, with its only content being the Ketchum paper. Shortly after publication, the paper was analyzed and outlined by Sharon Hill of Doubtful News for the Committee for Skeptical Inquiry. Hill reported on the questionable journal, mismanaged DNA testing and poor quality paper, stating that "The few experienced geneticists who viewed the paper reported a dismal opinion of it noting it made little sense." "The Scientist" magazine also analyzed the paper, reporting that:


title: Bigfoot

text: A body print taken in the year 2000 from the Gifford Pinchot National Forest in Washington state dubbed the Skookum cast is also believed by some to have been made by a Bigfoot that sat down in the mud to eat fruit left out by researchers during the filming of an episode of the "Animal X" television show. Skeptics believe the cast to have been made by a known animal such as an elk.


title: Bigfoot

text: Anthropologist Jeffrey Meldrum, who specializes in the study of primate bipedalism, possesses over 300 footprint casts that he maintains could not be made by wood carvings or human feet based on their anatomy, but instead are evidence of a large, non-human primate present today in America.


title: Bigfoot

text: In 2005, Matt Crowley obtained a copy of an alleged Bigfoot footprint cast, called the "Onion Mountain Cast", and was able to painstakingly recreate the dermal ridges. Michael Dennett of the "Skeptical Inquirer" spoke to police investigator and primate fingerprint expert Jimmy Chilcutt in 2006 for comment on the replica and he stated, "Matt has shown artifacts can be created, at least under laboratory conditions, and field researchers need to take precautions". Chilcutt had previously stated that some of the alleged Bigfoot footprint plaster casts he examined were genuine due to the presence of "unique dermal ridges". Dennett states that Chilcutt had published nothing on the statements about "unique dermal ridges" that Chilcutt states prove authenticity, nor had anyone else published anything on that topic, with Chilcutt making his statements solely through a posting on the Internet. Dennett states further that no reviews on Chilcutt's statements had been performed beyond those by what Dennett states to be "other Bigfoot enthusiasts".


title: Bigfoot

text: In 2015, Centralia College professor Michael Townsend claimed to have discovered prey bones with "human-like" bite impressions on the southside of Mount St. Helens. Townsend claimed the bites were over two times wider than a human bite, and that he and two of his students also found 16-inch footprints in the area.


title: Bigfoot

text: Jeremiah Byron, host of the "Bigfoot Society Podcast", believes Bigfoot are omnivores, stating, "They eat both plants and meat. I've seen accounts that they eat everything from berries, leaves, nuts, and fruit to salmon, rabbit, elk, and bear. Ronny Le Blanc, host of "Expedition Bigfoot" on the Travel Channel indicated he has heard anecdotal reports of Bigfoot allegedly hunting and consuming deer.


title: Bigfoot

text: Claims about the origins and characteristics of Bigfoot have also crossed over with other paranormal claims, including that Bigfoot, extraterrestrials, and UFOs are related or that Bigfoot creatures are psychic, can cross into different dimensions, or are completely supernatural in origin. Additionally, claims regarding Bigfoot have been associated with conspiracy theories including a government cover-up.


title: Bigfoot

text: The most well-known video of an alleged Bigfoot, the "Patterson-Gimlin" film, was recorded on October 20, 1967, by Roger Patterson and Robert "Bob" Gimlin as they explored an area called Bluff Creek in Northern California. The 59.5-second-long video has become an iconic piece of Bigfoot lore, and continues to be a highly scrutinized, analyzed, and debated subject.


title: Bigfoot

text: Academic experts from related fields have typically judged the film as providing "no supportive data of any scientific value" with perhaps the most common proposed explanation being that it was a hoax.


title: Bigfoot

text: There are several organizations dedicated to the research and investigation of Bigfoot sightings in the United States. The oldest and largest is the Bigfoot Field Researchers Organization (BFRO). The BFRO also provides a free database to individuals and other organizations. Their website includes reports from across North America that have been investigated by researchers to determine credibility. Another includes the North American Wood Ape Conservancy (NAWAC), a nonprofit organization. Other similar organizations exist throughout many U.S. states and their members come from a variety of backgrounds.


title: Bigfoot

text: Some organizations, as well as private researchers and enthusiasts own and operate Bigfoot museums. In 2022, The Bigfoot Crossroads of America Museum and Research Center in Hastings, Nebraska was selected for addition into the archives of the U.S. Library of Congress.


title: Bigfoot

text: Conferences and festivals dedicated to Bigfoot are attended by thousands of people. These events commonly include guest speakers, research and lore presentations, and sometimes live music, vendors, food trucks, and other activities such as costume contests and "Bigfoot howl" competitions. The Chamber of Commerce in Willow Creek, California has hosted the "Bigfoot Daze" festival annually since the 1960s, drawing on the popularity of the local lore. Some receive collaboration between local government and corporations, such as the Smoky Mountain Bigfoot Festival in Townsend, Tennessee which is sponsored by Monster Energy. The 2022 Bigfoot Festival in Marion, North Carolina saw tens of thousands in attendance, resulting in a large economic boost for the small town of less than 8,000 residents.


title: Bigfoot

text: In February 2016, the University of New Mexico at Gallup held a two-day Bigfoot conference at a cost of $7,000 in university funds.


title: Bigfoot

text: Bigfoot has a demonstrable impact in popular culture, and has been compared to Michael Jordan as a cultural icon. In 2018, "Smithsonian" magazine declared "Interest in the existence of the creature is at an all-time high". According to a poll taken in May 2020, about 1 in 10 American adults believe that Bigfoot is a real animal. The creature has inspired the naming of a medical company, music festival, sports mascot, amusement park ride, monster truck, a Marvel Comics superhero and more. In 2022, A Bigfoot named "Legend" was selected as the official mascot for the World Athletics Championships being held in Eugene, Oregon. October 20, the anniversary of the Patterson-Gimlin film recording, is considered by some as "National Sasquatch Awareness Day".


title: Bigfoot

text: Laws and ordinances exist regarding harming or killing a Bigfoot, specifically in the state of Washington. In 1969 in Skamania County, a law was passed making killing a Bigfoot punishable by a felony conviction resulting in a monetary fine up to $10,000 or five years imprisonment. In 1984, the law was amended to a misdemeanor and the entire county was declared a "Sasquatch refuge". Whatcom County followed suit in 1991, declaring the county a "Sasquatch Protection and Refuge Area". In 2022, Grays Harbor County, Washington, passed a similar resolution after a local elementary school in Hoquiam submitted a classroom project asking for a "Sasquatch Protection and Refuge Area" to be granted. In 2021, Rep. Justin Humphrey, in an effort to bolster tourism, proposed an official Bigfoot hunting season in Oklahoma, indicating that the Wildlife Conservation Commission would regulate permits and the state would offer a $3 million bounty if such a creature was captured alive and unharmed.


title: Bigfoot

text: In 2015, World Champion taxidermist Ken Walker completed what he believes to be a lifelike Bigfoot model based on the subject in the Patterson–Gimlin film. He entered it into the 2015 World Taxidermy & Fish Carving Championships in Springfield, Missouri and was the subject of Dan Wayne's 2019 documentary "Big Fur".


title: Bigfoot

text: Some have been critical of Bigfoot's rise to fame, arguing that the appearance of the creatures in cartoons, reality shows, and advertisements further reduces the potential validity of serious scientific research. Others propose that society's fascination with the concept of Bigfoot stems from human interest in mystery, the paranormal, and loneliness. In a 2022 article discussing recent Bigfoot sightings, journalist John Keilman of the "Chicago Tribune" states, "As UFOs have gained newfound respect, becoming the subject of a Pentagon investigative panel, the alleged Bigfoot sighting is a reminder that other paranormal phenomena are still out there, entrancing true believers and amusing skeptics".


title: Bigfoot

text: In the 2018 podcast "Wild Thing", creator and journalist Laura Krantz argues that the concept of Bigfoot can be an important part of environmental interest and protection, stating, "If you look at it from the angle that Bigfoot is a creature that has eluded capture or hasn't left any concrete evidence behind, then you just have a group of people who are curious about the environment and want to know more about it, which isn't that far off from what naturalists have done for centuries". Bigfoot has been used in official government environmental protection campaigns, albeit comedically, by entities such as the U.S. Forest Service in 2015.


title: Bigfoot

text: The act of searching for or researching the creatures is often referred to as "Squatching" or "Squatch'n", popularized by the Animal Planet reality series, "Finding Bigfoot". Bigfoot researchers and believers are often called "Squatchers".


title: Bigfoot

text: During the onset of the COVID-19 pandemic, Bigfoot became a part of many North American social distancing promotion campaigns, with the creature being referred to as the "Social Distancing Champion" and as the subject of various internet memes related to the pandemic.


title: Fourier transform

text: A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, which will output a function depending on temporal frequency or spatial frequency respectively. That process is also called "analysis". An example application would be decomposing the waveform of a musical chord into terms of the intensity of its constituent pitches. The term "Fourier transform" refers to both the frequency domain representation and the mathematical operation that associates the frequency domain representation to a function of space or time.


title: Fourier transform

text: The Fourier transform of a function is a complex-valued function representing the complex sinusoids that comprise the original function. For each frequency, the magnitude (absolute value) of the complex value represents the amplitude of a constituent complex sinusoid with that frequency, and the argument of the complex value represents that complex sinusoid's phase offset. If a frequency is not present, the transform has a value of 0 for that frequency. The Fourier transform is not limited to functions of time, but the domain of the original function is commonly referred to as the "time domain". The Fourier inversion theorem provides a "synthesis" process that recreates the original function from its frequency domain representation.


title: Fourier transform

text: Functions that are localized in the time domain have Fourier transforms that are spread out across the frequency domain and vice versa, a phenomenon known as the uncertainty principle. The critical case for this principle is the Gaussian function, of substantial importance in probability theory and statistics as well as in the study of physical phenomena exhibiting normal distribution (e.g., diffusion). The Fourier transform of a Gaussian function is another Gaussian function. Joseph Fourier introduced the transform in his study of heat transfer, where Gaussian functions appear as solutions of the heat equation.


title: Fourier transform

text: The Fourier transform can be formally defined as an improper Riemann integral, making it an integral transform, although this definition is not suitable for many applications requiring a more sophisticated integration theory. For example, many relatively simple applications use the Dirac delta function, which can be treated formally as if it were a function, but the justification requires a mathematically more sophisticated viewpoint.


title: Fourier transform

text: The Fourier transform can also be generalized to functions of several variables on Euclidean space, sending a function of 'position space' to a function of momentum (or a function of space and time to a function of 4-momentum). This idea makes the spatial Fourier transform very natural in the study of waves, as well as in quantum mechanics, where it is important to be able to represent wave solutions as functions of either position or momentum and sometimes both. In general, functions to which Fourier methods are applicable are complex-valued, and possibly vector-valued. Still further generalization is possible to functions on groups, which, besides the original Fourier transform on or (viewed as groups under addition), notably includes the discrete-time Fourier transform (DTFT, group = ), the discrete Fourier transform (DFT, group = ) and the Fourier series or circular Fourier transform (group = , the unit circle ≈ closed finite interval with endpoints identified). The latter is routinely employed to handle periodic functions. The fast Fourier transform (FFT) is an algorithm for computing the DFT.


title: Fourier transform

text: The Fourier transform is an extension of the Fourier series, which in its most general form introduces the use of complex exponential functions. For example, for a function formula_1, the amplitude and phase of a frequency component at frequency formula_2, is given by this complex number:


title: Fourier transform

text: The extension provides a frequency continuum of components formula_4 using an infinite integral of integration:


title: Fourier transform

text: Here, the transform of function formula_1 at frequency formula_6 is denoted by the complex number formula_7, which is just one of several common conventions. Evaluating for all values of formula_6 produces the "frequency-domain" function. When the independent variable (formula_9) represents "time" (often denoted by formula_10), the transform variable (formula_6) represents frequency (often denoted by formula_12). For example, if time is measured in seconds, then frequency is in hertz.


title: Fourier transform

text: A key to interpreting is that the effect of multiplying formula_1 by formula_14 is to subtract formula_6 from every frequency component of function formula_16 (also see Negative frequency) So the component that was at formula_6 ends up at zero hertz, and the integral produces its amplitude, because all the other components are oscillatory and integrate to zero over an infinite interval.


title: Fourier transform

text: The functions formula_12 and formula_19 are often referred to as a "Fourier transform pair".  A common notation for designating transform pairs is:


title: Fourier transform

text: And the Fourier transform extension is:The complex number, formula_7, conveys both amplitude and phase of frequency formula_6. So is a representation of formula_1 as a weighted summation of complex exponential functions. This is known as the Fourier inversion theorem, and was first introduced in Fourier's "Analytical Theory of Heat", although a proof by modern standards was not given until much later.


title: Fourier transform

text: For other common conventions and notations, including using the angular frequency instead of the ordinary frequency , see Other conventions and Other notations below. The Fourier transform on Euclidean space is treated separately, in which the variable often represents position and momentum. The conventions chosen in this article are those of harmonic analysis, and are characterized as the unique conventions such that the Fourier transform is both unitary on and an algebra homomorphism from to , without renormalizing the Lebesgue measure.


title: Fourier transform

text: Many other characterizations of the Fourier transform exist. For example, one uses the Stone–von Neumann theorem: the Fourier transform is the unique unitary intertwiner for the symplectic and Euclidean Schrödinger representations of the Heisenberg group.


title: Fourier transform

text: In 1822, Fourier claimed (see ) that any function, whether continuous or discontinuous, can be expanded into a series of sines. That important work was corrected and expanded upon by others to provide the foundation for the various forms of the Fourier transform used since.


title: Fourier transform

text: Although Fourier series can represent periodic waveforms as the sum of harmonically-related sinusoids, Fourier series can't represent "non-periodic" waveforms. However, the Fourier transform is able to represent "non-periodic" waveforms as well. It achieves this by applying a limiting process to lengthen the period of any waveform to infinity and then treating that as a periodic waveform.


title: Fourier transform

text: In the study of Fourier series, the Fourier coefficients represent the amplitude of each "harmonically-related" sinusoid present in the Fourier series of a periodic function . Similarly, the Fourier transform represents the amplitude and phase of every sinusoid present in a (possibly non-periodic) function .


title: Fourier transform

text: The Fourier transform uses an integral (or "continuous sum") that exploits properties of sine and cosine to recover the amplitude and phase of each sinusoid in a Fourier series. The inverse Fourier transform recombines these waves using a similar integral to reproduce the original function.


title: Fourier transform

text: To simplify the math, it is desirable to write the Fourier series as a sum of complex exponentials (see ). Each complex exponential or "complex sinusoid" of frequency can be expressed using Euler's formula as the sum of a cosine wave of frequency for the real component plus a sine wave also of frequency for the imaginary component:


title: Fourier transform

text: Expressing real sinusoids as complex sinusoids makes it necessary for the Fourier coefficients formula_26to be complex valued, but has the benefit of compactly representing all necessary information about each frequency. The usual interpretation of this complex number is that formula_27 (its magnitude) gives the amplitude and formula_28 (its argument) gives the phase of the complex sinusoid for that coefficient.


title: Fourier transform

text: These complex exponentials may have negative frequency. For example, both complex sinusoids and complete one cycle per unit of , but the first represents a positive frequency while the second represents a negative frequency. Positive frequency can be understood as rotating counter-clockwise about the complex plane while negative frequency can be understood as rotating clockwise about the complex plane. When complex sinusoids are interpreted as a helix in three-dimensions (with the third dimension being the imaginary component), negating the frequency simply changes the handedness of the helix.


title: Fourier transform

text: Real sine and cosine waves can be recovered from the complex exponential representation of sinusoids. For example, a corollary to Euler's formula allows expressing cosine and sine waves as either the real or imaginary part of a complex sinusoid or as a weighted sum of two complex sinusoids of opposite frequency:


title: Fourier transform

text: Consequently, a general form of any real sinusoid (with frequency , phase shift , and amplitude ) can be expressed as the sum of two complex sinusoids of opposite frequency ( and -) but equal magnitude () and with the phase shift embedded in both their complex coefficients:


title: Fourier transform

text: Hence, every real sinusoid (and real signal) can be considered to consist of a positive and negative frequency, whose imaginary components cancel but whose real components contribute equally to form the real signal.


title: Fourier transform

text: To avoid the use of complex numbers and negative frequencies, the sine and cosine transforms together can be used as an equivalent alternative form of the Fourier transform.


title: Fourier transform

text: There is a close connection between the definition of Fourier series and the Fourier transform for functions that are zero outside an interval. For such a function, we can calculate its Fourier series on any interval that includes the points where is not zero. The Fourier transform is also defined for such a function. As we increase the length of the interval in which we calculate the Fourier series, then the Fourier series coefficients begin to resemble the Fourier transform and the sum of the Fourier series of begins to resemble the inverse Fourier transform. More precisely, suppose is large enough that the interval contains the interval in which is not zero. Then, the th series coefficient is given by:


title: Fourier transform

text: since is zero outside . Thus, the Fourier coefficients are equal to the values of the Fourier transform sampled on a grid of width , multiplied by the grid width .


title: Fourier transform

text: Under appropriate conditions, the Fourier series of will equal the function . In other words, can be written:


title: Fourier transform

text: This second sum is a Riemann sum. By letting it will converge to the integral for the inverse Fourier transform as expressed above. Under suitable conditions, this argument may be made precise.


title: Fourier transform

text: The following figures provide a visual illustration how the Fourier transform measures whether a frequency is present in a particular function. The depicted function oscillates at 3 Hz (if measures seconds) and tends quickly to 0. (The second factor in this equation is an envelope function that shapes the continuous sinusoid into a short pulse. Its general form is a Gaussian function). This function was specially chosen to have a real Fourier transform that can be easily plotted. The first image contains its graph. In order to calculate formula_34 we must integrate . The second image shows the plot of the real and imaginary parts of this function. The real part of the integrand is almost always positive, because when is negative, the real part of is negative as well. Because they oscillate at the same rate, when is positive, so is the real part of . The result is that when you integrate the real part of the integrand you get a relatively large number (in this case ). On the other hand, when you try to measure a frequency that is not present, as in the case when we look at formula_35, you see that both real and imaginary component of this function vary rapidly between positive and negative values, as plotted in the third image. Therefore, in this case, the integrand oscillates fast enough so that the integral is very small and the value for the Fourier transform for that frequency is nearly zero.


title: Fourier transform

text: The general situation may be a bit more complicated than this, but this in spirit is how the Fourier transform measures how much of an individual frequency is present in a function .


title: Fourier transform

text: When the real and imaginary parts of a complex function are decomposed into their even and odd parts, there are four components, denoted below by the subscripts RE, RO, IE, and IO. And there is a one-to-one mapping between the four components of a complex time function and the four components of its complex frequency transform:


title: Fourier transform

text: Under suitable conditions on the function formula_12, it can be recovered from its Fourier transform formula_19. Indeed, denoting the Fourier transform operator by formula_49, so formula_50, then for suitable functions, applying the Fourier transform twice simply flips the function: formula_51, which can be interpreted as "reversing time". Since reversing time is two-periodic, applying this twice yields formula_52, so the Fourier transform operator is four-periodic, and similarly the inverse Fourier transform can be obtained by applying the Fourier transform three times: formula_53. In particular the Fourier transform is invertible (under suitable conditions).


title: Fourier transform

text: These equalities of operators require careful definition of the space of functions in question, defining equality of functions (equality at every point? equality almost everywhere?) and defining equality of operators – that is, defining the topology on the function space and operator space in question. These are not true for all functions, but are true under various conditions, which are the content of the various forms of the Fourier inversion theorem.


title: Fourier transform

text: This fourfold periodicity of the Fourier transform is similar to a rotation of the plane by 90°, particularly as the two-fold iteration yields a reversal, and in fact this analogy can be made precise. While the Fourier transform can simply be interpreted as switching the time domain and the frequency domain, with the inverse Fourier transform switching them back, more geometrically it can be interpreted as a rotation by 90° in the time–frequency domain (considering time as the -axis and frequency as the -axis), and the Fourier transform can be generalized to the fractional Fourier transform, which involves rotations by other angles. This can be further generalized to linear canonical transformations, which can be visualized as the action of the special linear group on the time–frequency plane, with the preserved symplectic form corresponding to the uncertainty principle, below. This approach is particularly studied in signal processing, under time–frequency analysis.


title: Fourier transform

text: The frequency variable must have inverse units to the units of the original function's domain (typically named or ). For example, if is measured in seconds, should be in cycles per second. If the scale of time is in units of 2 seconds, then another greek letter typically is used instead to represent angular frequency (where ) in units of radians per second. If using for units of length, then must be in inverse length, e.g., wavenumbers. That is to say, there are two versions of the real line: one which is the range of and measured in units of t, and the other which is the range of and measured in inverse units to the units of . These two distinct versions of the real line cannot be equated with each other. Therefore, the Fourier transform goes from one space of functions to a different space of functions: functions which have a different domain of definition.


title: Fourier transform

text: In general, must always be taken to be a linear form on the space of its domain, which is to say that the second real line is the dual space of the first real line. See the article on linear algebra for a more formal explanation and for more details. This point of view becomes essential in generalisations of the Fourier transform to general symmetry groups, including the case of Fourier series.


title: Fourier transform

text: That there is no one preferred way (often, one says "no canonical way") to compare the two versions of the real line which are involved in the Fourier transform—fixing the units on one line does not force the scale of the units on the other line—is the reason for the plethora of rival conventions on the definition of the Fourier transform. The various definitions resulting from different choices of units differ by various constants.


title: Fourier transform

text: Because formula_58, the alternative form formula_59 (which calls the non-unitary form in angular frequency) has no factor in its definition


title: Fourier transform

text: An alternative form formula_63 (which calls the unitary form in angular frequency) has a factor of formula_64 in its definition


title: Fourier transform

text: and also has that same factor of formula_64 in its corresponding inversion formula, producing a symmetrical relationship


title: Fourier transform

text: In other conventions, the Fourier transform has in the exponent instead of , and vice versa for the inversion formula. Effectively that defines  formula_68  as a negative frequency, because the corresponding spectral component is formula_69 But many of the identities involving the Fourier transform remain valid in those conventions, provided all terms that explicitly involve have it replaced by . To add further confusion, be aware that since electrical engineers use the letter to represent current, their form of the transform typically uses the letter for the imaginary unit instead of .


title: Fourier transform

text: When using dimensionless units, the constant factors might not even be written in the transform definition. For instance, in probability theory, the characteristic function of the probability density function of a random variable of continuous type is defined without a negative sign in the exponential, and since the units of are ignored, there is no 2 either:


title: Fourier transform

text: From the higher point of view of group characters, which is much more abstract, all these arbitrary choices disappear, as will be explained in the later section of this article, which treats the notion of the Fourier transform of a function on a locally compact Abelian group.


title: Fourier transform

text: The Fourier transform may be defined in some cases for non-integrable functions, but the Fourier transforms of integrable functions have several strong properties.


title: Fourier transform

text: However, formula_19 need not be integrable. For example, the Fourier transform of the rectangular function, which is integrable, is the sinc function, which is not Lebesgue integrable, because its improper integrals behave analogously to the alternating harmonic series, in converging to a sum without being absolutely convergent.


title: Fourier transform

text: It is not generally possible to write the "inverse transform" as a Lebesgue integral. However, when both and formula_19 are integrable, the inverse equality


title: Fourier transform

text: holds almost everywhere. That is, the Fourier transform is injective on . (But if is continuous, then equality holds for every .)


title: Fourier transform

text: Let and be integrable, and let and be their Fourier transforms. If "f"("x") and "g"("x") are also square-integrable, then the Parseval formula follows:


title: Fourier transform

text: Plancherel's theorem makes it possible to extend the Fourier transform, by a continuity argument, to a unitary operator on . On , this extension agrees with original Fourier transform defined on , thus enlarging the domain of the Fourier transform to (and consequently to for ). Plancherel's theorem has the interpretation in the sciences that the Fourier transform preserves the energy of the original quantity. The terminology of these formulas is not quite standardised. Parseval's theorem was proved only for Fourier series, and was first proved by Lyapunov. But Parseval's formula makes sense for the Fourier transform as well, and so even though in the context of the Fourier transform it was proved by Plancherel, it is still often referred to as Parseval's formula, or Parseval's relation, or even Parseval's theorem.


title: Fourier transform

text: See Pontryagin duality for a general formulation of this concept in the context of locally compact abelian groups.


title: Fourier transform

text: The Poisson summation formula (PSF) is an equation that relates the Fourier series coefficients of the periodic summation of a function to values of the function's continuous Fourier transform. The Poisson summation formula says that for sufficiently regular functions ,