title: Letter case

text: Other languages vary in their use of capitals. For example, in German all nouns are capitalised (this was previously common in English as well, mainly in the 17th and 18th centuries), while in Romance and most other European languages the names of the days of the week, the names of the months, and adjectives of nationality, religion, and so on normally begin with a lower-case letter. On the other hand, in some languages it is customary to capitalise formal polite pronouns, for example "De", "Dem" (Danish), "Sie", "Ihnen" (German), and "Vd" or "Ud" (short for "usted" in Spanish).


title: Letter case

text: Informal communication, such as texting, instant messaging or a handwritten sticky note, may not bother to follow the conventions concerning capitalisation, but that is because its users usually do not expect it to be formal.


title: Letter case

text: Similar orthographic and graphostylistic conventions are used for emphasis or following language-specific or other rules, including:


title: Letter case

text: In English-language publications, various conventions are used for the capitalisation of words in publication titles and headlines, including chapter and section headings. The rules differ substantially between individual house styles.


title: Letter case

text: The convention followed by many British publishers (including scientific publishers like "Nature" and "New Scientist", magazines like "The Economist", and newspapers like "The Guardian" and "The Times") and many U.S. newspapers is sentence-style capitalisation in headlines, i.e. capitalisation follows the same rules that apply for sentences. This convention is usually called "sentence case". It may also be applied to publication titles, especially in bibliographic references and library catalogues. An example of a global publisher whose English-language house style prescribes sentence-case titles and headings is the International Organization for Standardization (ISO).


title: Letter case

text: For publication titles it is, however, a common typographic practice among both British and U.S. publishers to capitalise significant words (and in the United States, this is often applied to headings, too). This family of typographic conventions is usually called "title case". For example, R. M. Ritter's "Oxford Manual of Style" (2002) suggests capitalising "the first word and all nouns, pronouns, adjectives, verbs and adverbs, but generally not articles, conjunctions and short prepositions". This is an old form of emphasis, similar to the more modern practice of using a larger or boldface font for titles. The rules which prescribe which words to capitalise are not based on any grammatically inherent correct–incorrect distinction and are not universally standardised; they differ between style guides, although most style guides tend to follow a few strong conventions, as follows:


title: Letter case

text: Title case is widely used in many English-language publications, especially in the United States. However, its conventions are sometimes not followed strictly especially in informal writing.


title: Letter case

text: In creative typography, such as music record covers and other artistic material, all styles are commonly encountered, including all-lowercase letters and special case styles, such as studly caps (see below). For example, in the wordmarks of video games it is not uncommon to use stylised upper-case letters at the beginning and end of a title, with the intermediate letters in small caps or lower case (e.g., , , and ).


title: Letter case

text: Single-word proper nouns are capitalised in formal written English, unless the name is intentionally stylised to break this rule (such as the first or last name of danah boyd).


title: Letter case

text: Multi-word proper nouns include names of organisations, publications, and people. Often the rules for "title case" (described in the previous section) are applied to these names, so that non-initial articles, conjunctions, and short prepositions are lowercase, and all other words are uppercase. For example, the short preposition "of" and the article "the" are lowercase in "Steering Committee of the Finance Department". Usually only capitalised words are used to form an acronym variant of the name, though there is some variation in this.


title: Letter case

text: With personal names, this practice can vary (sometimes all words are capitalised, regardless of length or function), but is not limited to English names. Examples include the English names Tamar of Georgia and Catherine the Great, "van" and "der" in Dutch names, "von" and "zu" in German, "de", "los", and "y" in Spanish names, "de" or "d'" in French names, and "ibn" in Arabic names.


title: Letter case

text: Some surname prefixes also affect the capitalisation of the following internal letter or word, for example "Mac" in Celtic names and "Al" in Arabic names.


title: Letter case

text: In the International System of Units (SI), a letter usually has different meanings in upper and lower case when used as a unit symbol. Generally, unit symbols are written in lower case, but if the name of the unit is derived from a proper noun, the first letter of the symbol is capitalised. Nevertheless, the "name" of the unit, if spelled out, is always considered a common noun and written accordingly in lower case. For example:


title: Letter case

text: For the purpose of clarity, the symbol for litre can optionally be written in upper case even though the name is not derived from a proper noun. For example, "one litre" may be written as:


title: Letter case

text: The letter case of a prefix symbol is determined independently of the unit symbol to which it is attached. Lower case is used for all submultiple prefix symbols and the small multiple prefix symbols up to "k" (for kilo, meaning 10 = 1000 multiplier), whereas upper case is used for larger multipliers:


title: Letter case

text: Some case styles are not used in standard English, but are common in computer programming, product branding, or other specialised fields.


title: Letter case

text: The usage derives from how programming languages are parsed, programmatically. They generally separate their syntactic tokens by simple whitespace, including space characters, tabs, and newlines. When the tokens, such as function and variable names start to multiply in complex software development, and there is still a need to keep the source code human-readable, Naming conventions make this possible. So for example, a function dealing with matrix multiplication might formally be called:


title: Letter case

text: In each case the capitalisation or lack thereof supports a different function. In the first, FORTRAN compatibility requires case-insensitive naming and short function names. The second supports easily discernible function and argument names and types, within the context of an imperative, strongly typed language. The third supports the macro facilities of LISP, and its tendency to view programs and data minimalistically, and as interchangeable. The fourth idiom needs much less syntactic sugar overall, because much of the semantics are implied, but because of its brevity and so lack of the need for capitalization or multipart words at all, might also make the code too abstract and overloaded for the common programmer to understand.


title: Letter case

text: Understandably then, such coding conventions are highly subjective, and can lead to rather opinionated debate, such as in the case of editor wars, or those about indent style. Capitalisation is no exception.


title: Letter case

text: Camel case: "theQuickBrownFoxJumpsOverTheLazyDog" or "TheQuickBrownFoxJumpsOverTheLazyDog" Spaces and punctuation are removed and the first letter of each word is capitalised. If this includes the first letter of the first word (CamelCase, "PowerPoint", "TheQuick...", etc.), the case is sometimes called upper camel case (or, illustratively, CamelCase), Pascal case in reference to the Pascal programming language or bumpy case.


title: Letter case

text: When the first letter of the first word is lowercase ("iPod", "eBay", "theQuickBrownFox..."), the case is usually known as lower camel case or dromedary case (illustratively: dromedaryCase). This format has become popular in the branding of information technology products and services, with an initial "i" meaning "Internet" or "intelligent", as in iPod, or an initial "e" meaning "electronic", as in email (electronic mail) or e-commerce (electronic commerce).


title: Letter case

text: Snake case: "the_quick_brown_fox_jumps_over_the_lazy_dog" Punctuation is removed and spaces are replaced by single underscores. Normally the letters share the same case (e.g. "UPPER_CASE_EMBEDDED_UNDERSCORE" or "lower_case_embedded_underscore") but the case can be mixed, as in OCaml modules. The style may also be called "pothole case", especially in Python programming, in which this convention is often used for naming variables. Illustratively, it may be rendered "snake_case", "pothole_case", etc. When all-upper-case, it may be referred to as "screaming snake case" (or "SCREAMING_SNAKE_CASE") or "hazard case".


title: Letter case

text: Kebab case: "the-quick-brown-fox-jumps-over-the-lazy-dog" Similar to snake case, above, except hyphens rather than underscores are used to replace spaces. It is also known as spinal case, param case, Lisp case in reference to the Lisp programming language, or dash case (or illustratively as kebab-case). If every word is capitalised, the style is known as train case ("TRAIN-CASE").


title: Letter case

text: Studly caps: e.g. "tHeqUicKBrOWnFoXJUmpsoVeRThElAzydOG" Mixed case with no semantic or syntactic significance to the use of the capitals. Sometimes only vowels are upper case, at other times upper and lower case are alternated, but often it is simply random. The name comes from the sarcastic or ironic implication that it was used in an attempt by the writer to convey their own coolness. It is also used to mock the violation of standard English case conventions by marketers in the naming of computer software packages, even when there is no technical requirement to do soe.g., Sun Microsystems' naming of a windowing system NeWS. Illustrative naming of the style is, naturally, random: "stUdlY cAps", "StUdLy CaPs", etc.


title: Letter case

text: In the character sets developed for computing, each upper- and lower-case letter is encoded as a separate character. In order to enable case folding and case conversion, the software needs to link together the two characters representing the case variants of a letter. (Some old character-encoding systems, such as the Baudot code, are restricted to one set of letters, usually represented by the upper-case variants.)


title: Letter case

text: Case-insensitive operations can be said to fold case, from the idea of folding the character code table so that upper- and lower-case letters coincide. The conversion of letter case in a string is common practice in computer applications, for instance to make case-insensitive comparisons. Many high-level programming languages provide simple methods for case conversion, at least for the ASCII character set.


title: Letter case

text: Whether or not the case variants are treated as equivalent to each other varies depending on the computer system and context. For example, user passwords are generally case sensitive in order to allow more diversity and make them more difficult to break. In contrast, case is often ignored in keyword searches in order to ignore insignificant variations in keyword capitalisation both in queries and queried material.


title: Letter case

text: Unicode defines case folding through the three case-mapping properties of each character: upper case, lower case, and title case (in this context, "title case" relates to ligatures and digraphs encoded as mixed-case single characters, in which the first component is in upper case and the second component in lower case). These properties relate all characters in scripts with differing cases to the other case variants of the character.


title: Letter case

text: As briefly discussed in Unicode Technical Note #26, "In terms of implementation issues, any attempt at a unification of Latin, Greek, and Cyrillic would wreak havoc [and] make casing operations an unholy mess, in effect making all casing operations context sensitive […]". In other words, while the shapes of letters like A, B, E, H, K, M, O, P, T, X, Y and so on are shared between the Latin, Greek, and Cyrillic alphabets (and small differences in their canonical forms may be considered to be of a merely typographical nature), it would still be problematic for a multilingual character set or a font to provide only a "single" code point for, say, uppercase letter B, as this would make it quite difficult for a wordprocessor to change that single uppercase letter to one of the three different choices for the lower-case letter, the Latin b (U+0062), Greek β (U+03B2) or Cyrillic в (U+0432). Therefore, the corresponding Latin, Greek and Cyrillic upper-case letters (U+0042, U+0392 and U+0412, respectively) are also encoded as separate characters, despite their appearance being basically identical. Without letter case, a "unified European alphabet"such as ABБCГDΔΕЄЗFΦGHIИJ...Z, with an appropriate subset for each languageis feasible; but considering letter case, it becomes very clear that these alphabets are rather distinct sets of symbols.


title: Letter case

text: Most modern word processors provide automated case conversion with a simple click or keystroke. For example, in Microsoft Office Word, there is a dialog box for toggling the selected text through UPPERCASE, then lowercase, then Title Case (actually start caps; exception words must be lowercased individually). The keystroke does the same thing.


title: Letter case

text: C and C++, as well as any C-like language that conforms to its standard library, provide these functions in the file ctype.h:


title: Letter case

text: Case conversion is different with different character sets. In ASCII or EBCDIC, case can be converted in the following way, in C:


title: Letter case

text: This only works because the letters of upper and lower cases are spaced out equally. In ASCII they are consecutive, whereas with EBCDIC they are not; nonetheless the upper-case letters are arranged in the same pattern and with the same gaps as are the lower-case letters, so the technique still works.


title: Letter case

text: Some computer programming languages offer facilities for converting text to a form in which all words are capitalised. Visual Basic calls this "proper case"; Python calls it "title case". This differs from usual title casing conventions, such as the English convention in which minor words are not capitalised.


title: Letter case

text: Originally alphabets were written entirely in majuscule letters, spaced between well-defined upper and lower bounds. When written quickly with a pen, these tended to turn into rounder and much simpler forms. It is from these that the first minuscule hands developed, the half-uncials and cursive minuscule, which no longer stayed bound between a pair of lines. These in turn formed the foundations for the Carolingian minuscule script, developed by Alcuin for use in the court of Charlemagne, which quickly spread across Europe. The advantage of the minuscule over majuscule was improved, faster readability.


title: Letter case

text: In Latin, papyri from Herculaneum dating before 79 CE (when it was destroyed) have been found that have been written in old Roman cursive, where the early forms of minuscule letters "d", "h" and "r", for example, can already be recognised. According to papyrologist Knut Kleve, "The theory, then, that the lower-case letters have been developed from the fifth century uncials and the ninth century Carolingian minuscules seems to be wrong." Both majuscule and minuscule letters existed, but the difference between the two variants was initially stylistic rather than orthographic and the writing system was still basically unicameral: a given handwritten document could use either one style or the other but these were not mixed. European languages, except for Ancient Greek and Latin, did not make the case distinction before about 1300.


title: Letter case

text: Traditionally, certain letters were rendered differently according to a set of rules. In particular, those letters that began sentences or nouns were made larger and often written in a distinct script. There was no fixed capitalisation system until the early 18th century. The English language eventually dropped the rule for nouns, while the German language keeps it.


title: Letter case

text: Similar developments have taken place in other alphabets. The lower-case script for the Greek alphabet has its origins in the 7th century and acquired its quadrilinear form (that is, characterised by ascenders and descenders) in the 8th century. Over time, uncial letter forms were increasingly mixed into the script. The earliest dated Greek lower-case text is the Uspenski Gospels (MS 461) in the year 835. The modern practice of capitalising the first letter of every sentence seems to be imported (and is rarely used when printing Ancient Greek materials even today).


title: Letter case

text: The individual type blocks used in hand typesetting are stored in shallow wooden or metal drawers known as "type cases". Each is subdivided into a number of compartments ("boxes") for the storage of different individual letters.


title: Letter case

text: The "Oxford Universal Dictionary on Historical Advanced Proportional Principles" (reprinted 1952) indicates that "case" in this sense (referring to the box or frame used by a compositor in the printing trade) was first used in English in 1588. Originally one large case was used for each typeface, then "divided cases", pairs of cases for majuscules and minuscules, were introduced in the region of today's Belgium by 1563, England by 1588, and France before 1723.


title: Letter case

text: The terms "upper" and "lower" case originate from this division. By convention, when the two cases were taken out of the storage rack and placed on a rack on the compositor's desk, the case containing the capitals and small capitals stood at a steeper angle at the back of the desk, with the case for the small letters, punctuation, and spaces being more easily reached at a shallower angle below it to the front of the desk, hence upper and lower case.


title: Letter case

text: Though pairs of cases were used in English-speaking countries and many European countries in the seventeenth century, in Germany and Scandinavia the single case continued in use.


title: Letter case

text: Various patterns of cases are available, often with the compartments for lower-case letters varying in size according to the frequency of use of letters, so that the commonest letters are grouped together in larger boxes at the centre of the case. The compositor takes the letter blocks from the compartments and places them in a composing stick, working from left to right and placing the letters upside down with the nick to the top, then sets the assembled type in a galley.


title: Ford Ranger

text: Ford Ranger is a nameplate that has been used on multiple model lines of pickup trucks sold by Ford worldwide. The nameplate has been used for distinct model lines of vehicles worldwide since 1982 from the compact and mid-size pickup category.


title: Ford Ranger

text: The Ford Ranger debuted as a compact pickup mainly sold in North America since 1982 for the 1983 model year, with later introductions in some South American countries. Between 1998 and 2011, the Ranger nameplate is also used for models that was developed by Mazda for sale outside the North American market. In 2011, Ford introduced the first Ranger based on the T6 platform. Considered a mid-size pickup truck, the model was developed in-house by Ford Australia. In the same year, the North American-market Ranger was discontinued, leaving the T6 platform-based Ranger as the sole Ranger model worldwide.


title: Ford Ranger

text: For the 2019 model year, the Ranger was reintroduced in North America using the globally-marketed T6 model. It is produced at the Michigan Assembly Plant at Wayne, Michigan. The Ranger is currently slotted below the F-150 and above the Maverick in the Ford North American pickup truck range, while for markets outside the Americas it is typically the only Ford pickup offered for sale.


title: Ford Ranger

text: The second generation of the T6-based Ranger was released in 2021 for worldwide markets, using the same T6 platform with revisions.


title: Ford Ranger

text: Prior to its use on compact pickup trucks, Ford used the Ranger nameplate on three different model lines. The Edsel division was the first to use the name, with the Edsel Ranger introduced in 1958 as its lowest-trim sedan; the model line lasted through the 1960 demise of the Edsel brand.


title: Ford Ranger

text: For 1965, the Ranger name returned to use by Ford as a trim package for F-Series trucks; in 1972, a corresponding Bronco Ranger was introduced. Offered through the 1981 model year, the Ranger trim served as the mid-level to high-level trim package.


title: Ford Ranger

text: Following the 1981 model year, the Ranger trim line was withdrawn from its light trucks, largely in anticipation of its 1983 model year compact pickup truck which was introduced in early 1982.


title: Ford Ranger

text: For the 1983 model year, Ford introduced the Ranger for the United States and Canada. The first compact pickup truck designed by Ford, the American-produced Ranger replaced the Mazda-produced Ford Courier. Produced across three generations using a single chassis architecture, the model line was marketed from the 1983 to the 2012 model years (ending retail sales after the 2011 model year).


title: Ford Ranger

text: The Ranger light-truck chassis architecture served as the basis for a wide range of vehicles over its production. Along with sharing body and powertrain components with the Ford Bronco II and Ford Explorer SUVs, the Ranger also shared components with the Ford Aerostar minivan and the Ford Explorer Sport Trac mid-size pickup truck. Through the use of rebadging, from 1994 to 2009, Mazda marketed the Ford Ranger in the United States and Canada as the Mazda B-Series (the reverse of the 1970s Ford Courier and also the reverse of the Ford Ranger outside of North America).


title: Ford Ranger

text: While among the highest-selling vehicles in the compact segment for nearly its entire 29-year production, an overall decline in demand for compact trucks led to its discontinuation after the 2011 model year (a short 2012 run was produced for fleet sales). On December 22, 2011, the final Ford Ranger produced for North America was assembled at the Twin Cities Assembly Plant, the final vehicle assembled at the facility.


title: Ford Ranger

text: For the 2019 model year, the Ranger returned to its model range in North America after an eight-year hiatus to slot below the F-Series. The first example was assembled on October 22, 2018. The first generation of the model line sold as a mid-size pickup truck, the fourth-generation Ranger is derived from the global-market Ranger T6 designed by Ford Australia with adaptations accommodate US government regulations along with other modifications made to match local market demands.


title: Ford Ranger

text: The current generation of the Ranger is offered in two configurations on a 127-inch wheelbase, including a 2+2 door SuperCab (6-foot bed) and a 4-door SuperCrew (5-foot bed). As of the current model, the two-door standard cab is not offered for sale in North America.


title: Ford Ranger

text: In 1995, exports of the Ranger began to select Latin and South American countries. To accommodate the demand for the vehicle, Ford Argentina commenced local production of the Ranger in 1998, introducing a four-door cab not sold in North America. During the 2000s, Rangers produced by Ford Argentina shared a common chassis with North American-produced vehicles, while offering a diesel engine option to meet local demand. For 2010, the locally-produced Ranger underwent a final exterior revision exclusive to the South American market.


title: Ford Ranger

text: Ford Argentina ended production of the compact Ranger following the 2011 model year to shift its production to its replacement, the mid-size Ranger T6.


title: Ford Ranger

text: In 1971, Ford entered the compact truck segment as it marketed the second-generation Mazda B series under the Ford Courier nameplate; the Courier was sold worldwide. For 1983, the Ranger replaced the Courier in North America, but Ford continued to source the Courier from Mazda for global markets into the 1990s, following the development of the B-Series model line. In 1998, Ford introduced the Ranger name on Mazda-sourced pickup trucks, however the Courier name continued through 2006 in Australia and New Zealand.


title: Ford Ranger

text: The first-generation Mazda-based Ranger was produced from 1998 to 2006, while the second generation was produced from 2006 to 2011; the latter was derived from the Mazda BT-50 (which replaced the Mazda B series). These Ranger models were sold in Asia, Australasia, Europe, Africa, and several Latin American markets.


title: Ford Ranger

text: In 2011, Ford introduced the first Ranger based on the T6 platform (codename: "P375"). Developed by Ford Australia, the T6-based Ranger replaced the American and Mazda-sourced Rangers with a single model, also forming a basis of the second-generation Mazda BT-50. The T6-based Ranger models are marketed worldwide, although it was not marketed in the United States and Canada between 2011 and 2018 model years. The second generation model of the T6-based Ranger (codename: "P703") was released in 2021, featuring major changes while riding on a revised T6 platform dubbed as "T6.2".


title: Jihyo

text: Park Ji-hyo (; born Park Ji-soo on February 1, 1997), known mononymously as Jihyo, is a South Korean singer. She is the leader and vocalist of the South Korean girl group Twice, formed by JYP Entertainment in 2015.


title: Jihyo

text: JYP Entertainment scouted Jihyo after she placed second in a contest on Junior Naver. She joined the company at the age of eight and trained for ten years, during which she became the face of Innisfree's teen line with boy band Boyfriend and trained with K-pop acts such as Wonder Girls' Sunmi and Hyerim, Bae Suzy, Jo Kwon, and Nichkhun. Jihyo was set to debut in a girl group with now-Twice members Nayeon, Jeongyeon and Sana, although the project was cancelled. Instead, she joined the reality television show "Sixteen", a competition to select the founding members of Twice. She legally changed her name to Jihyo before the competition. As one of nine successful participants, she went on to join the newly formed girl group Twice. Jihyo was voted by her bandmates as leader in an anonymous vote.


title: Jihyo

text: In October 2015, Twice officially debuted with the release of their first extended play (EP), "The Story Begins." Its lead single "Like Ooh-Ahh" became the first K-pop debut song to reach 100 million views on YouTube.


title: Jihyo

text: On March 6, 2022, Jihyo released her first OST titled "Stardust Love Song" for tvN's "Twenty-Five Twenty-One". She released her second OST titled "I Fly" for SBS's "Today's Webtoon" on July 29.


title: Jihyo

text: All song credits are adapted from the Korea Music Copyright Association's database unless stated otherwise.


title: Natalia Tena

text: Natalia Gastiain Tena (born 1 November 1984) is a British actress and musician. She is known for playing Nymphadora Tonks in the "Harry Potter" film series (2007-2011), and the wildling Osha in the HBO series "Game of Thrones" (2011-2013; 2016).


title: Natalia Tena

text: Tena is the lead singer and accordionist of Molotov Jukebox. The band released their debut album "Carnival Flower" (2014), in Spring 2014, featuring their single "Neon Lights". Their second studio album, "Tropical Gypsy" (2016), was released on 15 April 2016 and was preceded by its lead single, "Pineapple Girl". It was promoted on the band's Tropical Gypsy Tour in April and May 2016.


title: Natalia Tena

text: Natalia Gastiain Tena was born in London, the daughter of Spanish parents, María Tena, a secretary, and Jesús Andrew Gastiain, a carpenter. Her family is of Extremaduran and Basque origin, and she was raised in the United Kingdom. Tena is fluent in English and Spanish. She studied at the boarding school Bedales.


title: Natalia Tena

text: Tena was taught the piano by her mother at five years old, influenced by Chuck Berry's music. Afterwards, at 18, Tena moved back to London and busked on the London Underground. While working with a theatre group called KneeHigh, where they were allowed to pick an instrument to play, Tena decided to learn the accordion.


title: Natalia Tena

text: Tena made her professional debut as Ellie in "About a Boy" (2002), and began acting full-time in 2003. She has played lead roles in stage adaptations of "Gone to Earth" in 2004, and "Nights at the Circus" in 2006.


title: Natalia Tena

text: In 2007, Tena appeared in the film adaptation of "Harry Potter and the Order of the Phoenix" playing the character Nymphadora Tonks. Tena reprised this role in its sequels "Harry Potter and the Half-Blood Prince," in 2009, "Harry Potter and the Deathly Hallows – Part 1" in 2010 and "Part 2" in 2011.


title: Natalia Tena

text: She hosted a behind-the-scenes featurette entitled "Trailing Tonks" for the subsequent DVD and Blu-ray release, and is credited as producer and director of the featurette, in which she also performs an original Christmas-themed blues song on guitar, which she composed while working as a busker on the London Underground.


title: Natalia Tena

text: In 2011, she played a lead role in the Scottish Film "You Instead". She also appeared as Osha in HBO's "Game of Thrones". In March 2013, she starred in the official music video for Lapalux's single "Without You (ft. Kerry Leatham)".


title: Natalia Tena

text: In 2014, Tena co-starred as a mentally ill woman in the "Black Mirror" Christmas episode "White Christmas".


title: Natalia Tena

text: In 2015, she starred as the lead, Jennifer Preston, in the British mini-series "Residue". In 2017, Tena was cast as Sara Morten in the CBS drama "Wisdom of the Crowd".


title: Natalia Tena

text: In April 2018, it was announced that Tena was cast in the series regular role of Lana Pierce on the YouTube science fiction series "Origin".


title: Punta Cana

text: Punta Cana is a resort town in the easternmost region of the Dominican Republic. It is part of the Veron–Punta Cana municipal district, in the Higüey municipality of La Altagracia Province. According to the 2010 census, this district had a population of 43,982 inhabitants.


title: Punta Cana

text: Punta Cana is the second-most popular tourist destination in Latin America, with more visitors than any other city in the Caribbean region. The Punta Cana International Airport (PUJ) is located about 3 km inland, on the highway that leads from Higüey to La Romana. This airport receives 64% of all flights that arrive in the Dominican Republic, receiving more passengers than the Las Américas International Airport, located in Santo Domingo, the country's capital.


title: Punta Cana

text: The area is known for its white sand beaches, blue turquoise waters, and balnearios which face both the Caribbean Sea and the Atlantic Ocean. The weather is hot for most of the year, especially in late summer and autumn when the Northern Tropics receive their most direct sunlight.


title: Punta Cana

text: The Punta Cana area has an estimated population of 100,000, with an annual growth rate of 11% as of 2011. To the north, it borders the village and beach of Cabeza de Toro, and the Bávaro and El Cortecito beaches. The nearest city, the 500-year-old Higüey, is away, which takes about an hour to reach by car. European entrepreneurs, particularly Spanish hotel chains, own all but two of the over 50 megaresorts at the Punta Cana tourism destination.


title: Punta Cana

text: The province’s coastline tends to be mildly windy. The ocean waters are mainly shallows, with several natural marine pools in which visitors can bathe without danger. From north to south, the main beaches are Uvero Alto, Macao, Arena Gorda, Bávaro, El Cortecito, Las Corales, and Cabeza de Toro, all north of the cape; and Cabo Engaño, Punta Cana, and Juanillo south of the cape.


title: Punta Cana

text: Bávaro is the area starting from Cabeza de Toro until Macao Beach. As the hotels started to rise along the east coast, Bavaro itself became a center of services with shopping malls, fast-food stores, drug stores, fine restaurants, banks, clinics, workshops, supermarkets, and schools. The major town in the district is Veron, now bigger than Higüey in territory, a spontaneous – and poor – urban development running along the original road from the west. Verón, last name of the French proprietor of a timberline business in the early 1930s, is now the base-city for hotel workers and related. It has, besides Bávaro, one of only four gas stations in Punta Cana: the next one is located west in Higüey, at the Fruisa crossroads; a new Texaco gas station opened in April 2010, south of Macao beach; and the new Shell gas station close to the airport (on the highway Coral) opened at the end of 2010.


title: Punta Cana

text: Punta Cana Village, with a population of about 15,000, is being developed by a master plan of the Punta Cana Group. In 1969 the area was purchased by this organization and development began in the following decades. The main avenue, Boulevard Primero de Noviembre, is lined with low office buildings. Branching off are streets with gated communities on both sides. To the east are single family residences. Small apartment buildings are to the west. A shopping area is near the airport and beyond the apartment houses is a mall and several stores. East of the village is the Westin Resort and golf course by the ocean. There is a public beach, Playa Blanca, with a shuttle bus from the Village's sole hotel. An upscale planned community, Cap Cana, is south of Punta Cana Village.


title: Punta Cana

text: Punta Cana features a tropical wet and dry climate under the Köppen climate classification. The weather is fairly consistent all year, with an average temperature of . The hot and humid season lasts from May to October, and during the day temperatures might reach . From November to March, temperatures during the evening are around .


title: Punta Cana

text: In the late 1960s, Frank Rainieri, a Dominican entrepreneur in his 20s and Theodore Kheel, a high-powered New York attorney and labor mediator teamed up with other investors, to acquire a 58-million square meter lot on the eastern end of the Dominican Republic. The area that is known today as Punta Cana was mostly an undeveloped coastal area of La Altagracia province. At the time the closest major city, Higüey, was a 5-hour drive. Their first project was a 40 guest hotel called the Punta Cana Club. In 1970, Rainieri changed the original name of the place, Yauya or Punta Borrachos, for Punta Cana. In 1978, the Paris Mediterranean Club joined the Grupo Punta Cana SA project, building a 350-room hotel within the project. Later, the Barceló and Newco Group settled in the Bavaro area.


title: Punta Cana

text: In 1979, the Hotel Puntacana was built and then in 1984, the Punta Cana International Airport was inaugurated, while more infrastructures such as highways were developed. In 1993, construction began on the Marina de Punta Cana Resort & Club marina. In 1996, the Dominican designer Óscar de la Renta and the Spanish singer Julio Iglesias joined the project. In 2000, the first of the residential community developments began and six years later Tortuga Bay opened.


title: Punta Cana

text: Corporate environmental and social responsibilities and policies have been pursued since the resort was built. The Puntacana Foundation- made of the Ecological Foundation and Community Services- has a 1,500-acre reserve that now serves as a research base for universities and a sanctuary for endangered species and has opened two schools- the Ann & Ted Kheel Polytechnic and the Puntacana International School- and a free health clinic in the local community of Véron.


title: Punta Cana

text: Bávaro was conceived as a town for the workers of the Punta Cana tourist complex, but it has been transformed into an important center for tourist services after the hotel expansion to the north of Punta Cana around Bávaro beach. Throughout the area there are dozens of hotels such as Riu, Iberostar, Be Live Grand Punta Cana, Meliá, Barceló, Palladium, Catalonia or Bahía Príncipe. The area also has several nightclubs such as: Oro at Hard Rock Hotel, Imagine, and Coco Bongo or Pachá.


title: Punta Cana

text: Numerous tourist attractions have been installed, some of a certain size such as the Manatí Park in Bávaro, a water park with manatees, dolphins and other kinds of animals. For tourists, the Punta Cana beach area is more popular because it is more affordable at international prices. Among the best-known digital magazines and newspapers in the entire eastern area are: BavaroDigital and BavaroMagazine. It is connected by road with Higüey and La Otra Banda. It extends about 15 km north to Playa Macao. Other nearby beaches are: Uvero Alto, Roco Ki and La Vacama. Bavaro has 10 km of beaches. The XII Ibero-American Summit was held on this site on November 15 and 16, 2002, where the heads of state and government of 21 Spanish and Portuguese-speaking nations met.


title: Punta Cana

text: The area has a low population density with the majority of the inhabitants being Haitian migrant workers. In 2010, Haitians represented 81.1 percent of the total population.


title: Punta Cana

text: Punta Cana is a tourist destination, and the area is a key contributor to tourism in the Dominican Republic.


title: Punta Cana

text: Many of the excursions in Punta Cana are near the water, it being a beach destination. These activities include snorkeling, windsurfing, banana boat rides, speedboats, scuba diving, catamaran cruises, party boats, deep sea fishing, as well as swimming with dolphins and sharks and snorkeling with stingrays. For visitors who prefer to see more of the Dominican countryside, there are land-based excursions such as safari tours, horseback riding and dune buggies.


title: Punta Cana

text: Visiting the Dominican Republic's smaller Caribbean islands of Saona and Catalina is a day trip from Punta Cana. The capital city Santo Domingo, and Los Haitises National Park, Samaná, are within a couple of hours. The Basilica Catholic Monument, built in 1962 and designed by two French architects, is in nearby Higüey, the 500-year-old capital of the province.


title: Punta Cana

text: The electricity is powered by Consorcio Energetico Punta Cana Macao (CEPM), a fossil fuel, renewable, and biomass energy producer led by US-based Argentine businessman Rolando Gonzalez-Bunster.


title: Punta Cana

text: Because of its location at the Caribbean Sea, diving is one of the tourist activities. The marine area surrounding Punta Cana was declared a marine reserve in 2012.


title: Punta Cana

text: The Punta Cana International Airport is the primary airport. In 2014, Punta Cana received over 2.4 million passengers, making it the second-busiest airport in the Caribbean. Grupo Puntacana built the Punta Cana International Airport in 1984 to facilitate tourism in the area. It was the western hemisphere’s first privately owned international airport.


title: Heap (data structure)

text: In computer science, a heap is a specialized tree-based data structure which is essentially an almost complete tree that satisfies the heap property: in a "max heap", for any given node C, if P is a parent node of C, then the "key" (the "value") of P is greater than or equal to the key of C. In a "min heap", the key of P is less than or equal to the key of C. The node at the "top" of the heap (with no parents) is called the "root" node.


title: Heap (data structure)

text: The heap is one maximally efficient implementation of an abstract data type called a priority queue, and in fact, priority queues are often referred to as "heaps", regardless of how they may be implemented. In a heap, the highest (or lowest) priority element is always stored at the root. However, a heap is not a sorted structure; it can be regarded as being partially ordered. A heap is a useful data structure when it is necessary to repeatedly remove the object with the highest (or lowest) priority, or when insertions need to be interspersed with removals of the root node.


title: Heap (data structure)

text: A common implementation of a heap is the binary heap, in which the tree is a binary tree (see figure). The heap data structure, specifically the binary heap, was introduced by J. W. J. Williams in 1964, as a data structure for the heapsort sorting algorithm. Heaps are also crucial in several efficient graph algorithms such as Dijkstra's algorithm. When a heap is a complete binary tree, it has a smallest possible height—a heap with "N" nodes and "a" branches for each node always has log "N" height.


title: Heap (data structure)

text: Note that, as shown in the graphic, there is no implied ordering between siblings or cousins and no implied sequence for an in-order traversal (as there would be in, e.g., a binary search tree). The heap relation mentioned above applies only between nodes and their parents, grandparents, etc. The maximum number of children each node can have depends on the type of heap.


title: Heap (data structure)

text: For a binary heap, in the array, the first index contains the root element. The next two indices of the array contain the root's children. The next four indices contain the four children of the root's two child nodes, and so on. Therefore, given a node at index , its children are at indices and , and its parent is at index . This simple indexing scheme makes it efficient to move "up" or "down" the tree.


title: Heap (data structure)

text: Balancing a heap is done by sift-up or sift-down operations (swapping elements which are out of order). As we can build a heap from an array without requiring extra memory (for the nodes, for example), heapsort can be used to sort an array in-place.


title: Heap (data structure)

text: After an element is inserted into or deleted from a heap, the heap property may be violated, and the heap must be re-balanced by swapping elements within the array.


title: Heap (data structure)

text: Although different type of heaps implement the operations differently, the most common way is as follows:


title: Heap (data structure)

text: Construction of a binary (or "d"-ary) heap out of a given array of elements may be performed in linear time using the classic Floyd algorithm, with the worst-case number of comparisons equal to 2"N" − 2"s"("N") − "e"("N") (for a binary heap), where "s"("N") is the sum of all digits of the binary representation of "N" and "e"("N") is the exponent of 2 in the prime factorization of "N". This is faster than a sequence of consecutive insertions into an originally empty heap, which is log-linear.


title: Armored Core

text: Several story continuities exist, spread across 13 main games, seven spin-offs, and three remastered re-releases. The first game in the series, "Armored Core", was released in 1997, while the most recent, "Armored Core VI: Fires of Rubicon", will be released in 2023. The series has been released on the PlayStation, PlayStation 2, PlayStation Portable, PlayStation 3, PlayStation Vita, Xbox 360, and Mobile Phone.


title: Armored Core

text: In the original continuity established by 1997's "Armored Core" through 2001's "", Earth experienced a cataclysm known as the "Great Destruction" and humanity has been forced underground. Corporations begin fighting for dominance, leading to the increasing reliance on Armored Core pilots called Ravens. Following the events of 1999's "", humanity rebuilds and colonizes Mars. Through 2000's "Armored Core 2" and its expansion, "Another Age", the fledgling Earth government struggles to maintain power as opportunistic corporations exploit the power gap and rebel groups resist against the hegemony of government and business interests.


title: Armored Core

text: The series was rebooted with 2002's "Armored Core 3", beginning a new story arc that concluded with "" in 2005. Following a global nuclear war, humanity has retreated underground. Following centuries of rule by an artificial intelligence called The Controller, its decay leads to the destruction of much of humanity's underground network, causing them to look toward the surface for safety. By the end of 2003's "", humanity has fully returned to the surface of Earth. The final two games of this continuity, 2004's "" and 2005's "Armored Core: Last Raven" involve the end of the existing power dynamic of corporations and Ravens fighting over the surface.


title: Armored Core

text: 2006's "Armored Core 4" rebooted the series yet again. Here, corporations have seized control of Earth governments and are waging war across the surface for dominance. A war waged over the course of the game pollutes the environment, leading to the creation of floating cities in 2008's "". Depending on the player's choices, humanity either barely survives the fallout of "For Answer's" conflict or is completely eradicated.


title: Armored Core

text: The final story arc of the series was introduced with 2012's "Armored Core V". A single corporation has dominance over a contaminated Earth and is being opposed by a resistance faction that seeks to overthrow them. 2013's "" details the outbreak of another war 100 years later following an apocalyptic event.


title: Armored Core

text: Within the core games of the franchise, the gameplay is generally focused on the player taking the role of a mech-piloting mercenary, taking on missions for various clients and gaining currency from completing them. Missions can involve multiple objectives and pit the player against computer controlled opponents, some of which pilot mechs as well. Upon completion of a mission, the operating costs of the mech, such as repairs and ammunition, are deducted from the total earnings of the player. If the player loses a mission, those same deductions occur from the player's direct balance.


title: Armored Core

text: The game's mechs, called Armored Cores, are highly customizable with hundreds of parts and weapons that can be purchased from an in-game shop or by fulfilling certain requirements. Different parts can provide gameplay advantages in certain terrains or against certain enemies, which forces the player to put thought into how to approach the construction of their mech. Many of the franchise's games feature a branching storyline where taking on certain missions can block off others, with consequences of a player's decision in mission being relayed to them at the end of a mission.


title: Armored Core

text: An Arena mode introduced in "" gave players the opportunity to fight opponents outside of missions for additional rewards. "Project Phantasma" also introduced the import feature, allowing players to retain their progress from a previous entry when starting a new one. This import feature would become a mainstay of the franchise, with "expansion" titles like "Silent Line: Armored Core" allowing for importing save data.


title: Armored Core

text: Since its first release, the "Armored Core" games have featured multiplayer options in some form. In the original PlayStation era, local split-screen multiplayer modes were the primary method, generally featuring head-to-head battles. A PlayStation Link Cable feature, allowing for the connection of two PlayStation consoles, was included in all three original "Armored Core" titles.


title: Armored Core

text: With the PlayStation 2, split-screen and console linking continue to be the primary source of multiplayer. 2004's "Armored Core: Nexus" introduced the LAN multiplayer mode, in addition to connecting through their internet service and allowed up to 4 players to fight in matches together.


title: Armored Core

text: Online multiplayer was first introduced in the Japanese released of "Armored Core 2: Another Age", but was removed in other regions due to the PlayStation Network Adapter not being ready in time. No PlayStation 2-era game after this release would include online play either, with the first game to do so being "Armored Core 4".


title: Armored Core

text: The original trilogy of "Armored Core" games were developed for the original PlayStation by FromSoftware and established many of the core themes and mechanics that would be found in the rest of the series. The debut title, "Armored Core", was released on July 10, 1997 in Japan. Story elements like corporate-funded conflicts, post-apocalyptic settings, and silent protagonists were introduced in the first game. The game's mechanics revolve around taking on missions from various clients for pay, using earned money to customize the player's Armored Core unit.


title: Armored Core

text: "" was released as a stand-alone expansion to the original game, released on December 4, 1997. "Project Phantasma" introduced an Arena mechanic that would be expanded on in later titles, as well as an import mechanic that would become an important feature through the franchise. Players were able to import save data from earlier "Armored Core" games and bring their existing Armored Core units into the expansions.


title: Armored Core

text: A second stand-alone expansion, "", was released on February 4, 1999 and was the final game released for the original PlayStation. It concluded the core arc of the original "Armored Core" and greatly expanded on the Arena mechanic introduced in "Project Phantasma". Like its predecessor, "Master of Arena" allowed players to import save files from both the original "Armored Core" and "Project Phantasma" to continue their progress.


title: Armored Core

text: All three games from the original PlayStation era were re-released on the PlayStation Network in 2007 for the tenth anniversary of the original title. The original "Armored Core" was also released on the Japanese PlayStation Classic in 2018.


title: Armored Core

text: With the transition to the PlayStation 2, FromSoftware released "Armored Core 2" as a launch title in Japan on August 3, 2000. As a narrative sequel to the original trilogy, "Armored Core 2" transitioned the series away from the post-apocalyptic setting and added more science fiction elements, such as Mars colonization. Much of the gameplay remained the same, including the mission structure, customization, and Arena modes. The title did overhaul the visuals from the original game, taking advantage of the added power of the new console, but overall designs stayed similar. Unlike "Project Phantasma" and "Master of Arena", players could not import their saves to the new game.


title: Armored Core

text: "" was released on April 12, 2001 as a stand-alone expansion. It allowed players to import their save files from "Armored Core 2" and continue with their existing Armored Core units. The game introduced movement controls using the DualShock analog sticks and cooperative mission mode. The Japanese version of "Armored Core 2" was the first title to include online broadband play, allowing players to fight each other over the internet.


title: Armored Core

text: "Armored Core 3" was released on April 4, 2002 and served as a reboot for the franchise. The story returned to a post-apocalyptic setting and retained the core concept of corporate warfare and mercenary mission structure. Very little gameplay was changed from the earlier PlayStation 2 titles, instead focusing on incremental improvements and minor features like USB mice, computer-controlled allies, and surround sound. Due to its nature as a reboot, players could not import save data from "Armored Core 2" or "Another Age".


title: Armored Core

text: A stand-alone expansion, "", was released on January 23, 2003 and was a direct sequel to "Armored Core 3". Like other expansions in the franchise, players could import their progress from "Armored Core 3" into "Silent Line", retaining their parts and credits from the earlier game. "Silent Line" introduced new gameplay mechanics, including computer-controlled companions and a first person mode.


title: Armored Core

text: "" was released on March 18, 2004 as a direct sequel to "Silent Line". Unlike its predecessor, "Nexus" was treated as a core entry rather than an expansion and did not allow for save data import. The game was the first in the franchise to include support for dual analog sticks. It also introduced a new LAN multiplayer mode that allowed up to 4 players to participate in matches against each other.


title: Armored Core

text: "" was released on August 4, 2005 and served as the conclusion to "Armored Core 3's" story arc. The game is structured around a 24-hour clock that moves forward as missions progress. At the end of the 24-hour period, choices made by the player can alter the outcome of the plot. The game introduced a component damage system, allowing for individual parts to be broken in combat.


title: Armored Core

text: "Armored Core 4" was released on December 21, 2006 for the PlayStation 3, serving as another reboot for the franchise. An Xbox 360 version, the first instance of a main title in the franchise being released outside of the PlayStation ecosystem, was released on March 22, 2007. Gameplay in "Armored Core 4" has been sped up and streamlined from its predecessors in an attempt to make the game more accessible to new players. The game marks the first instance of online multiplayer outside of the Japanese release of "Armored Core 2: Another Age".


title: Armored Core

text: "" was released on March 19, 2008 as a standalone expansion to "Armored Core 4". It incorporates an online co-operative mode and a branching storyline. The game was noted for its technical problems on the PlayStation 3 version.


title: Armored Core

text: "Armored Core V" was released on January 26, 2012 for the PlayStation 3 and Xbox 360 and acts as indirect sequel to "Armored Core 4" and "Armored Core: For Answer". The game focuses on the online multiplayer component and includes far fewer offline story missions than its predecessors. In the game's online mode, players battle for territory in teams of up to 20 players. A co-operative mode is included for players to fight NPCs alongside other players for various rewards.


title: Armored Core

text: "" was released on September 24, 2013 as a standalone expansion to "Armored Core V". The game retains its predecessor's multiplayer focus, though it allows players to create teams of AI companions instead of requiring teams composed entirely of players. A full-length story mode returns alongside a newly implemented "hardcore mode", and players can import their saved games from "Armored Core V" to retain their personalized mechs.


title: Armored Core

text: "Armored Core VI: Fires of Rubicon" was announced at The Game Awards 2022 on December 8, 2022. The game will be released on PlayStation 4, PlayStation 5, Windows, Xbox One, and Xbox Series X/S in 2023.


title: Armored Core

text: In 2004, FromSoftware released two spin-offs from the main "Armored Core" series. The first, "" was released on October 28, 2004 for the PlayStation 2. Removing the focus from story-based missions, the game is instead built around an Arena mode where the player must compete with computer-controlled opponents to increase their rank. Minigames designed as training exercises were included to allow players to practice specific skills.


title: Armored Core

text: "" was released on December 12, 2004 for the PlayStation Portable. Like "Nine Breaker", its focus was on Arena-style gameplay, though a new mechanic put a focus on building an artificial intelligence strategy for the Armored Core units to execute. "Formula Front" was later released for the PlayStation 2 in Japan.


title: Armored Core

text: Several mobile games were released in the "Armored Core" franchise from 2004 to 2008, however they were never released outside of Japan. An American version of these mobile games was in development around 2005, but the title was never released.


title: Armored Core

text: "Armored Core: Tower City Blade" is a manga by Fujimi Shobo based on the game. It was serialized in "Dragon Age Pure" between March 14 and April 14, 2007. A project called "Armored Core: Fort Tower Song" was to consist of a book and an anime also released in 2007. The book was completed but the anime was not. From Software announced in 2011 that the anime had been canceled due to View Works shutting down.


title: Armored Core

text: The making of "Armored Core" solidified FromSoftware's development skills, and in July 1999, they released the multiplayer action game "Frame Gride" for the Sega Dreamcast. The company's focus would shift from RPGs to mech games due in part to the success of the "Armored Core" series. In 2002, FromSoftware released the mech action game "" for the Xbox. In 2004, they released another Xbox title, "Metal Wolf Chaos." In 2005, FromSoftware would start to produce a series of licensed games based on the various anime properties under the banner "Another Century's Episode".


title: Confusion matrix

text: In the field of machine learning and specifically the problem of statistical classification, a confusion matrix, also known as an error matrix, is a specific table layout that allows visualization of the performance of an algorithm, typically a supervised learning one (in unsupervised learning it is usually called a matching matrix). Each row of the matrix represents the instances in an actual class while each column represents the instances in a predicted class, or vice versa – both variants are found in the literature. The name stems from the fact that it makes it easy to see whether the system is confusing two classes (i.e. commonly mislabeling one as another).


title: Confusion matrix

text: It is a special kind of contingency table, with two dimensions ("actual" and "predicted"), and identical sets of "classes" in both dimensions (each combination of dimension and class is a variable in the contingency table).


title: Confusion matrix

text: Given a sample of 12 individuals, 8 that have been diagnosed with cancer and 4 that are cancer-free, where individuals with cancer belong to class 1 (positive) and non-cancer individuals belong to class 0 (negative), we can display that data as follows:


title: Confusion matrix

text: Assume that we have a classifier that distinguishes between individuals with and without cancer in some way, we can take the 12 individuals and run them through the classifier. The classifier then makes 9 accurate predictions and misses 3: 2 individuals with cancer wrongly predicted as being cancer-free (sample 1 and 2), and 1 person without cancer that is wrongly predicted to have cancer (sample 9).


title: Confusion matrix

text: Notice, that if we compare the actual classification set to the predicted classification set, there are 4 different outcomes that could result in any particular column. One, if the actual classification is positive and the predicted classification is positive (1,1), this is called a true positive result because the positive sample was correctly identified by the classifier. Two, if the actual classification is positive and the predicted classification is negative (1,0), this is called a false negative result because the positive sample is incorrectly identified by the classifier as being negative. Third, if the actual classification is negative and the predicted classification is positive (0,1), this is called a false positive result because the negative sample is incorrectly identified by the classifier as being positive. Fourth, if the actual classification is negative and the predicted classification is negative (0,0), this is called a true negative result because the negative sample gets correctly identified by the classifier.


title: Confusion matrix

text: We can then perform the comparison between actual and predicted classifications and add this information to the table, making correct results appear in green so they are more easily identifiable.


title: Confusion matrix

text: The template for any binary confusion matrix uses the four kinds of results discussed above (true positives, false negatives, false positives, and true negatives) along with the positive and negative classifications. The four outcomes can be formulated in a 2×2 "confusion matrix", as follows:


title: Confusion matrix

text: The color convention of the three data tables above were picked to match this confusion matrix, in order to easily differentiate the data.


title: Confusion matrix

text: Now, we can simply total up each type of result, substitute into the template, and create a confusion matrix that will concisely summarize the results of testing the classifier:


title: Confusion matrix

text: In this confusion matrix, of the 8 samples with cancer, the system judged that 2 were cancer-free, and of the 4 samples without cancer, it predicted that 1 did have cancer. All correct predictions are located in the diagonal of the table (highlighted in green), so it is easy to visually inspect the table for prediction errors, as values outside the diagonal will represent them. By summing up the 2 rows of the confusion matrix, one can also deduce the total number of positive (P) and negative (N) samples in the original dataset, i.e. formula_1 and formula_2.


title: Confusion matrix

text: In predictive analytics, a table of confusion (sometimes also called a confusion matrix) is a table with two rows and two columns that reports the number of "true positives", "false negatives", "false positives", and "true negatives". This allows more detailed analysis than simply observing the proportion of correct classifications (accuracy). Accuracy will yield misleading results if the data set is unbalanced; that is, when the numbers of observations in different classes vary greatly.


title: Confusion matrix

text: For example, if there were 95 cancer samples and only 5 non-cancer samples in the data, a particular classifier might classify all the observations as having cancer. The overall accuracy would be 95%, but in more detail the classifier would have a 100% recognition rate (sensitivity) for the cancer class but a 0% recognition rate for the non-cancer class. F1 score is even more unreliable in such cases, and here would yield over 97.4%, whereas informedness removes such bias and yields 0 as the probability of an informed decision for any form of guessing (here always guessing cancer).


title: Confusion matrix

text: According to Davide Chicco and Giuseppe Jurman, the most informative metric to evaluate a confusion matrix is the Matthews correlation coefficient (MCC).


title: Confusion matrix

text: Confusion matrix is not limited to binary classification and can be used in multi-class classifiers as well. The confusion matrices discussed above have only two conditions: positive and negative. For example, the table below summarizes communication of a whistled language between two speakers, zero values omitted for clarity.


title: Footwear

text: Footwear refers to garments worn on the feet, which typically serves the purpose of protection against adversities of the environment such as wear from ground textures and temperature. Footwear in the manner of shoes therefore primarily serves the purpose to ease locomotion and prevent injuries. Footwear can also be used for fashion and adornment as well as to indicate the status or rank of the person within a social structure.


title: Footwear

text: Socks and other hosiery are typically worn additionally between the feet and other footwear for further comfort and relief.


title: Footwear

text: Cultures have different customs regarding footwear. These include not using any in some situations, usually bearing a symbolic meaning. This can however also be imposed on specific individuals to place them at a practical disadvantage against shod people, if they are excluded from having footwear available or are prohibited from using any. This usually takes place in situations of captivity, such as imprisonment or slavery, where the groups are among other things distinctly divided by whether or whether not footwear is being worn.


title: Footwear

text: In some cultures, people remove their shoes before entering a home. Bare feet are also seen as a sign of humility and respect, and adherents of many religions worship or mourn while barefoot. Some religious communities explicitly require people to remove shoes before they enter holy buildings, such as temples.


title: Footwear

text: In several cultures people remove their shoes as a sign of respect towards someone of higher standing. In a similar context deliberately forcing other people to go barefoot while being shod oneself has been used to clearly showcase and convey one's superiority within a setting of power disparity.


title: Footwear

text: Footwear has been in use since the earliest human history, archeological finds of complete shoes date back to the Chalcolithic (ca. 5000 BCE).


title: Footwear

text: The Romans saw clothing and footwear as unmistakable signs of power and status in society, and most Roman citizens wore footwear, while slaves and peasants sometimes remained barefoot. The Middle Ages saw the rise of high-heeled shoes, also associated with power, and the desire to look larger than life, and artwork from that period often depicts bare feet as a symbol of poverty. Depictions of captives such as prisoners or slaves from the same period well into the 18th century show the individuals barefooted almost exclusively, at this contrasting the prevailing partakers of the scene. Officials like prosecutors, judges but also slave owners or passive bystanders were usually portrayed wearing shoes.


title: Footwear

text: During the Middle Ages, men and women wore pattens, commonly seen as the predecessor of the modern high-heeled shoe, while the poor and lower classes in Europe, as well as slaves in the New World, were usually barefoot. In the 15th century, chopines were created in Turkey, and were usually high. These shoes became popular in Venice and throughout Europe, as a status symbol revealing wealth and social standing.


title: Footwear

text: During the 16th century, royalty such as Catherine de Medici and Mary I of England began wearing high-heeled shoes to make them look taller or larger than life. By 1580, men also wore them, and a person with authority or wealth might be described as, "well-heeled". In modern society, high-heeled shoes are a part of women's fashion and are widespread in certain countries around the world.


title: Footwear

text: Modern footwear is usually made up of leather or plastic, and rubber. In fact, leather was one of the original materials used for the first versions of a shoe. The soles can be made of rubber or plastic, sometimes having a sheet of metal inside. Roman sandals had sheets of metal on their soles so that it would not bend out of shape.


title: Footwear

text: More recently, footwear providers like Nike, have begun to source environmentally friendly materials.


title: Footwear

text: In Europe, the footwear industry has declined in the last years. Whereas in 2005, there were about 27,000 firms, in 2008 there were only 24,000. As well as the number of firms, the direct employment has decreased. The only factors that remained almost steady was the value added at factor cost and production value.


title: Footwear

text: In the U.S., the annual footwear industry revenue was $48 billion in 2012. In 2015, there were about 29,000 shoe stores in the U.S. and the shoe industry employed about 189,000 people. Due to rising imports, these numbers are also declining. The only way of staying afloat in the shoe market is to establish a presence in niche markets.


title: Footwear

text: To ensure high quality and safety of footwear, manufacturers have to make sure all products comply to existing and relevant standards. By producing footwear in accordance with national and international regulations, potential risks can be minimized and the interest of both textile manufacturers and consumers can be protected.


title: Footwear

text: Footwear can create two types of impressions: two-dimensional and three-dimensional impressions. When footwear places material onto a solid surface, it creates a two-dimensional impression. These types of impressions can be made with a variety of substances, like dirt and sand. When footwear removes material from a soft surface, it creates a three-dimensional impression. These types of impressions can be made in a variety of soft substances, like snow and dirt. Two-dimensional impressions also differ from three-dimensional impressions because the latter demonstrate length, width, and depth whereas two-dimensional impressions only demonstrate the first two aspects.


title: My Three Sons

text: My Three Sons is an American television sitcom that aired from September 29, 1960, to April 13, 1972. The series was broadcast on ABC during its first five seasons, before moving to CBS for the remaining seasons. "My Three Sons" chronicles the life of widower and aeronautical engineer Steven Douglas (Fred MacMurray) as he raises his three sons.


title: My Three Sons

text: The series originally featured William Frawley (who had first co-starred with Fred MacMurray 25 years earlier in the film "Car 99") as the boys' maternal grandfather and live-in housekeeper, William Michael Francis "Bub" O'Casey. William Demarest, playing Bub's brother, "Uncle Charley", replaced Frawley in 1965 because of Frawley's declining health. In September 1965 (when the show moved from ABC to CBS and began to be filmed in color), eldest son Mike (Tim Considine) married fiancée Sally Ann Morrison (Meredith MacRae), and his character was written out of the show. To keep the emphasis on "three sons", original youngest son Chip's (Stanley Livingston) friend Ernie (Barry Livingston) was adopted. In the program's later years, Steven Douglas married Barbara Harper (Beverly Garland) and adopted her young daughter Dorothy Anne ("Dodie") (Dawn Lyn).


title: My Three Sons

text: The series was a cornerstone of the ABC and CBS lineups in the 1960s. Disney producer Bill Walsh often mused on whether the concept of the show was inspired by the film "The Shaggy Dog", as in his view they shared "the same dog, the same kids, and Fred MacMurray".


title: My Three Sons

text: The show began on ABC in black-and-white. The first season, consisting of 36 episodes, was directed in its entirety by Peter Tewksbury, who produced and occasionally scripted the programs.


title: My Three Sons

text: During the 1964 fall season, William Frawley, who played Bub, was declared too ill to work by Desilu Studios, as the company was informed that insuring the actor would be too costly. Frawley continued in the role until a suitable replacement could be found at midseason. He was replaced by William Demarest, who played his hard-nosed brother (great) Uncle Charley, introduced partway through the 1964–1965 season (the last on ABC). According to the storyline, Bub returns to Ireland to help his Aunt Kate celebrate her 104th birthday. Soon after, brother Charley visits and stays on. Charley, a cello-playing merchant sailor, was a soft-hearted curmudgeon, who proved to be a responsible caregiver. Frawley left the series before the end of the 1964–1965 season. He died March 3, 1966.


title: My Three Sons

text: The address of the fictional home in Bryant Park was 837 Mill Street. The phone number was LArson 0-6719, rotary dialed as 520-6719 (from Season 1, Episode 25 - 'Off Key' first aired March 16, 1961). The actual address of the home used for the Bryant Park episodes was 837 5th Avenue in Los Angeles California. The neighboring driveway to the right of the house was used as the Douglas' driveway on the show, although the real life driveway for that home is on the left hand side of the house. The fictional phone number for a neighboring home was 527-3601 Season 1, Episode 26 - Small Adventure aired March 23, 1961. Many of the 1960s "My Three Sons" external shoots were actually done on location on 5th Avenue, and many items, such as the two young trees growing across the street on early episodes, were still visible in 2022.


title: My Three Sons

text: Peter Tewksbury directed the first season. The succeeding director, Richard Whorf, took over the reins for one season and was in turn followed by former actor-turned-director Gene Reynolds from 1962 to 1964. James V. Kern, an experienced Hollywood television director who had previously helmed the "Hollywood" and "Europe" episodes of "I Love Lucy", continued in this role for two years until his untimely death at 57 in late 1966. Director James Sheldon was also contracted to finish episodes that had been partly completed by Kern to complete that season. Fred De Cordova was the show's longest and most consistent director of the series (108 episodes) until he left in 1971 to produce "The Tonight Show Starring Johnny Carson". Earl Bellamy rounded out the series as director of the show's final year.


title: My Three Sons

text: "My Three Sons" moved to the CBS television network for the 1965–1966 season after ABC declined to underwrite the expense of producing the program in color. Along with the change in networks and the transition to color, Tim Considine (who had earlier worked with Fred MacMurray on "The Shaggy Dog"), playing eldest son Mike, had chosen not to renew his contract due to a clash with executive producer Don Fedderson over Considine's wish to direct but not co-star in the series. (Considine did, however, direct one of the last black-and-white episodes for ABC.) In an August 1989 interview on the "Pat Sajak Show", he explained that he was also devoted to car racing, which his contract forbade. His character was written out, along with Meredith MacRae, who had played his fiancée Sally, in a wedding episode that was the premiere of the 1965–1966 season on CBS. After this episode, Mike is mentioned briefly in only four succeeding episodes (including the one in which the family adopts Ernie) and is never seen again, even at Robbie's and Steve's weddings. (Steve explains briefly in one of these episodes that he has another son who "lives away from home".) In the episode "Steve and the Huntress" (first aired January 27, 1966), Mike is specifically mentioned as teaching at a college. MacRae joined "Petticoat Junction" the following year, the last of three actresses to play Billie Jo Bradley.


title: My Three Sons

text: To keep the show's title plausible, the show's head writer, George Tibbles, fashioned a three-part story arc in which an orphaned friend of youngest brother Richard (Chip, played by Stanley Livingston), Ernie Thompson (played by his real-life brother, Barry Livingston), awaits adoption when his current foster parents are transferred to the Orient. Steve offers to adopt Ernie, but faces antagonism from Uncle Charley, who finds Ernie a bit grating and forecasts major headaches over both the boy and his dog. It also transpires that a law requires a woman to live in the home of an adoptive family. A likable female social worker supervises the case and the Douglases speculate that Steve might marry the woman to make the adoption possible, but they agree that this is not reason enough for them to be married. Also, the family has no need for a housekeeper; Uncle Charley already has things running smoothly. The family soon appears before a judge who researches the law and determines that its intent is to ensure that a full-time caregiver is in the household. As Charley meets that role and has had a change of heart about Ernie, he assents to a legal fiction that declares him the Douglas family's "housemother".


title: My Three Sons

text: While the three sons were always central to the storyline, several major changes took place by the late 1960s. In the spring of 1967, the series' ratings began to sag, and it finished its seventh season in 31st place in the Nielsen ratings. It was decided that the 1967–1968 season would bring the program not only a new time slot but also new storylines to spice up the ratings. In the fall of 1967, CBS moved "My Three Sons" to Saturday at 8:30 pm ET. In the season premiere episode, "Moving Day", the Douglas family and Uncle Charley relocate from the fictional Midwestern town of Bryant Park to Los Angeles, California. Robbie (Don Grady) marries his girlfriend Katie Miller. Katie is played by Tina Cole, who had appeared in different roles on three previous episodes: "House For Sale" from the fourth season (February 13, 1964), "The Coffee House Set" from the fifth season (November 19, 1964), and "Robbie and the Little Stranger" from the sixth season (February 17, 1966). At the end of the 1967–1968 season, the ratings had improved from the previous year with the series placing at 24th in the Nielsens. The following season, the newlyweds discover that Katie is pregnant and she gives birth to triplets named Robert, Steven, and Charles. Originally played by sets of uncredited twins, the boys were later played uncredited by Guy, Gunnar, and Garth Swanson; and in the last two seasons by Michael, Daniel, and Joseph Todd.


title: My Three Sons

text: The following year in the 10th season, 1969–1970, Steve remarries. His new bride, widowed teacher Barbara Harper (Beverly Garland), brings with her a five-year-old daughter, Dorothy "Dodie" (Dawn Lyn), whom Steve adopts. Dodie is wary of Steve at first, believing that he wants her to just forget her late father, but he explains that he wants her to always remember and love him, but since he's no longer alive, Steve wants to raise her in his place and he hopes she'll come to love him, too. The series' last year and a half feature fewer appearances from both Don Grady and Stanley Livingston. Grady's character was written out at the end of the 11th season, which allowed for his wife Katie and their triplet sons to remain in the Douglas household for the following season (as a structural engineer Robbie was working on a bridge construction in Peru). Meanwhile, Chip and his teenage wife Polly (Ronne Troup), who had eloped after Polly's disciplinarian father refused to sanction their marriage, move into their own apartment.


title: My Three Sons

text: At the end of the 1970–1971 season, the show's 11th year, "My Three Sons" was still garnering healthy ratings. By the spring of 1971, it had finished in 19th place. A 1971 television pilot with Don Grady and Tina Cole called "Three of a Kind", then retitled "Robbie"—about Robbie, Katie, and the triplets moving to San Francisco—was filmed but not picked up as a series. The final episode of the 1970–1971 season, "After the Honeymoon", actually set up the premise for this pilot. Richard X. Slattery and Pat Carroll guest-starred as the landlords of the apartment block into which Robbie and Katie move. However, Don Grady had informed the producers of his intention to leave the series and pursue a new full-time career as a composer, which he ultimately did.


title: My Three Sons

text: For the series' 12th and, ultimately, final season, CBS moved the show to Mondays at 10:00 pm ET. In addition to the time changes for the 12th season, a new four-part story arc is introduced with MacMurray in a second role, that of his cousin, the Laird (Lord) Fergus McBain Douglas of Sithian Bridge; English actor Alan Caillou's voice was dubbed over MacMurray's. The plot centers on Lord Douglas's arrival in Los Angeles from the family's native Scotland, in search of a bride to take back to Scotland with him.


title: My Three Sons

text: He finds Terri Dowling (Anne Francis), a waitress at the Blue Berry Bowling Alley. While initially reluctant to give up her life in America and return to Scotland as nobility, she finally accepts. This storyline continues a plot idea that originally began in the fourth season, when the Douglases visited Scotland on the pretense of having been told they had inherited a castle in the Highlands.


title: My Three Sons

text: With a later time slot, the show finished the season outside the top 30. To save the series, CBS moved it in midseason back to Thursdays at 8:30 pm ET, its old time slot. Nevertheless, "My Three Sons" ended its primetime run in the spring of 1972 after 12 years on the air. CBS also aired daytime reruns starting in September 1971 (only the CBS color shows), for about one season.


title: My Three Sons

text: "My Three Sons" had 36 episodes each in the first two seasons. The series had at least thirty episodes in each of the first eight seasons; the episode output then decreased by two episodes until the eleventh season, which had twenty-four episodes, along with the twelfth season. The first five seasons were filmed in black & white, then after the move to CBS, it was filmed in color for the remainder of its run.


title: My Three Sons

text: The series was initially filmed at Desilu Studios in Hollywood, but at the start of the 1967–68 season, the cast and crew began filming the series at the CBS Studio Center in Studio City, California. The reasons behind this move concerned the sale of actress-comedian Lucille Ball's studios to the Gulf + Western conglomerate, which owned Paramount Pictures, so Don Fedderson Productions, who produced "My Three Sons" (along with "Family Affair" starring Brian Keith), had to quickly make other arrangements for filming.


title: My Three Sons

text: Although Don Fedderson gets the credit, "My Three Sons" was created by George Tibbles and produced by Don Fedderson Productions throughout the show's run, with MCA Television co-distributing the series during its 1960–65 ABC airing. When the series moved to CBS in 1965, the latter network assumed full production responsibilities (in association with Fedderson Productions) until the end of the series in 1972. CBS now holds the series' copyright. CBS Television Distribution presently owns distribution rights to the entire series (including the more widely seen and aforementioned 1965–72 CBS episodes). The show did not get syndicated until September 1976, when Viacom Enterprises assumed off-network distribution (although CBS did air reruns of the show in its daytime lineup from December 1971 until the fall of 1972), and even then, only the CBS color episodes aired, while the black and white ABC episodes did not air on broadcast TV at all. At the time, the first half of season 11 was in the same syndication package as seasons 6-10, while season 12 and the second half of season 11 were distributed with seasons 1–5.


title: My Three Sons

text: Nick at Nite aired "My Three Sons" from November 3, 1985, to October 28, 1991, with episodes from Seasons 1–5, the second half of season 11, and season 12. The Family Channel also aired only the black and white episodes from September 7, 1992, to July 30, 1993. The Seasons 1–3 episodes had the original Chevrolet closing credits. The Seasons 6–10 (and the first half of season 11) episodes were later aired on TV Land in the late 1990s. Odyssey ran all of the color episodes in the early 2000s. They also briefly aired the black and white episodes. In 2000, TV Land briefly aired the black & white episodes again, using the same syndication episode rights that were on Nick at Nite during the 1980s. In 2006 the Retro Television Network broadcast the show. Only seasons 6-10 and the first half of season 11 were aired.


title: My Three Sons

text: In 2009, FamilyNet began airing the program as a lead-in for its "Happy Days" and "Family Ties" program block, which ended in February 2010. From 2012 to 2014, and also from October 2015-February 2016, MeTV aired the Season 6-10 episodes in heavy rotation, and most closing credits included the original sponsor tags, such as those for Kellogg's. In 2016, Decades began airing the CBS (color) episodes in its "binge" blocks on some weekends.


title: My Three Sons

text: MeTV began airing the black and white episodes on May 29, 2017, the first time the black and white episodes have aired on broadcast television since their original ABC airings. MeTV aired all episodes in order until August 3, 2018, when the series's last episode aired. This marks the first time a U.S. television station aired the entire series in full. MeTV started reairing the entire series again on August 6, 2018 and has continued to do so ever since.


title: My Three Sons

text: MacMurray and most of the cast took part in "Thanksgiving Reunion with The Partridge Family and My Three Sons", which aired on ABC on November 25, 1977. The retrospective special looked back at the history of "My Three Sons" and "The Partridge Family" (other than featuring single parents with a large family, the two series had no narrative, or even a studio, link). The special was notable for featuring footage from early black and white episodes of "My Three Sons" that, at this point in time, were not in syndication. While most of the collected casts gathered in a studio to reminisce, Demarest appeared in a brief pre-taped segment.


title: My Three Sons

text: CBS DVD (distributed by Paramount) has released the first five seasons of "My Three Sons" on DVD in Region 1.


title: My Three Sons

text: In most episodes, the soundtrack was edited to remove the background musical score, which were originally stock music from the Capitol Records library; the licensing agreement with Capitol only covered broadcast rights, not home video rights, and clearing the music for home video release with the individual composers who worked on the Capitol recordings was deemed cost-prohibitive. The Capitol scores were replaced instead with more modern, synthesized music. The original theme tune by Frank DeVol has been left unaltered; his musical scores in later seasons of the show, written specifically for the series, would less-likely be affected by licensing problems if the later seasons were released on DVD.


title: My Three Sons

text: On May 13, 2019, the third season was released, in two volume sets, available exclusively through Amazon's made-on-demand (MOD) service. Season 4 was released on September 10, 2019 and season 5 on December 17, 2019.


title: Hexagon

text: In geometry, a hexagon (from Greek , , meaning "six", and , , meaning "corner, angle") ou sexagon (from Latin , meaning "six") is a six-sided polygon or 6-gon creating the outline of a cube. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°.


title: Hexagon

text: A "regular hexagon" has Schläfli symbol {6} and can also be constructed as a truncated equilateral triangle, t{3}, which alternates two types of edges.


title: Hexagon

text: A regular hexagon is defined as a hexagon that is both equilateral and equiangular. It is bicentric, meaning that it is both cyclic (has a circumscribed circle) and tangential (has an inscribed circle).


title: Hexagon

text: The common length of the sides equals the radius of the circumscribed circle or circumcircle, which equals formula_1 times the apothem (radius of the inscribed circle). All internal angles are 120 degrees. A regular hexagon has six rotational symmetries ("rotational symmetry of order six") and six reflection symmetries ("six lines of symmetry"), making up the dihedral group D. The longest diagonals of a regular hexagon, connecting diametrically opposite vertices, are twice the length of one side. From this it can be seen that a triangle with a vertex at the center of the regular hexagon and sharing one side with the hexagon is equilateral, and that the regular hexagon can be partitioned into six equilateral triangles.


title: Hexagon

text: Like squares and equilateral triangles, regular hexagons fit together without any gaps to "tile the plane" (three hexagons meeting at every vertex), and so are useful for constructing tessellations. The cells of a beehive honeycomb are hexagonal for this reason and because the shape makes efficient use of space and building materials. The Voronoi diagram of a regular triangular lattice is the honeycomb tessellation of hexagons. It is not usually considered a triambus, although it is equilateral.


title: Hexagon

text: The maximal diameter (which corresponds to the long diagonal of the hexagon), "D", is twice the maximal radius or circumradius, "R", which equals the side length, "t". The minimal diameter or the diameter of the inscribed circle (separation of parallel sides, flat-to-flat distance, short diagonal or height when resting on a flat base), "d", is twice the minimal radius or inradius, "r". The maxima and minima are related by the same factor:


title: Hexagon

text: For any regular polygon, the area can also be expressed in terms of the apothem "a" and the perimeter "p". For the regular hexagon these are given by "a" = "r", and "p"formula_5, so


title: Hexagon

text: If a regular hexagon has successive vertices A, B, C, D, E, F and if P is any point on the circumcircle between B and C, then .


title: Hexagon

text: It follows from the ratio of circumradius to inradius that the height-to-width ratio of a regular hexagon is 1:1.1547005; that is, a hexagon with a long diagonal of 1.0000000 will have a distance of 0.8660254 between parallel sides.


title: Hexagon

text: For an arbitrary point in the plane of a regular hexagon with circumradius formula_8, whose distances to the centroid of the regular hexagon and its six vertices are formula_9 and formula_10


title: Hexagon

text: If formula_10 are the distances from the vertices of a regular hexagon to any point on its circumcircle, then


title: Hexagon

text: The "regular hexagon" has D symmetry. There are 16 subgroups. There are 8 up to isomorphism: itself (D), 2 dihedral: (D D), 4 cyclic: (Z, Z, Z, Z) and the trivial (e)


title: Hexagon

text: These symmetries express nine distinct symmetries of a regular hexagon. John Conway labels these by a letter and group order. r12 is full symmetry, and a1 is no symmetry. p6, an isogonal hexagon constructed by three mirrors can alternate long and short edges, and d6, an isotoxal hexagon constructed with equal edge lengths, but vertices alternating two different internal angles. These two forms are duals of each other and have half the symmetry order of the regular hexagon. The i4 forms are regular hexagons flattened or stretched along one symmetry direction. It can be seen as an elongated rhombus, while d2 and p2 can be seen as horizontally and vertically elongated kites. g2 hexagons, with opposite sides parallel are also called hexagonal parallelogons.


title: Hexagon

text: Each subgroup symmetry allows one or more degrees of freedom for irregular forms. Only the g6 subgroup has no degrees of freedom but can seen as directed edges.


title: Hexagon

text: Hexagons of symmetry g2, i4, and r12, as parallelogons can tessellate the Euclidean plane by translation. Other hexagon shapes can tile the plane with different orientations.


title: Hexagon

text: The 6 roots of the simple Lie group , represented by a Dynkin diagram , are in a regular hexagonal pattern. The two simple roots have a 120° angle between them.


title: Hexagon

text: The 12 roots of the Exceptional Lie group G2, represented by a Dynkin diagram are also in a hexagonal pattern. The two simple roots of two lengths have a 150° angle between them.


title: Hexagon

text: Coxeter states that every zonogon (a 2"m"-gon whose opposite sides are parallel and of equal length) can be dissected into parallelograms. In particular this is true for regular polygons with evenly many sides, in which case the parallelograms are all rhombi. This decomposition of a regular hexagon is based on a Petrie polygon projection of a cube, with 3 of 6 square faces. Other parallelogons and projective directions of the cube are dissected within rectangular cuboids.


title: Hexagon

text: A regular hexagon has Schläfli symbol {6}. A regular hexagon is a part of the regular hexagonal tiling, {6,3}, with three hexagonal faces around each vertex.


title: Hexagon

text: A regular hexagon can also be created as a truncated equilateral triangle, with Schläfli symbol t{3}. Seen with two types (colors) of edges, this form only has D symmetry.


title: Hexagon

text: A truncated hexagon, t{6}, is a dodecagon, {12}, alternating two types (colors) of edges. An alternated hexagon, h{6}, is an equilateral triangle, {3}. A regular hexagon can be stellated with equilateral triangles on its edges, creating a hexagram. A regular hexagon can be dissected into six equilateral triangles by adding a center point. This pattern repeats within the regular triangular tiling.


title: Hexagon

text: A regular hexagon can be extended into a regular dodecagon by adding alternating squares and equilateral triangles around it. This pattern repeats within the rhombitrihexagonal tiling.


title: Hexagon

text: From bees' honeycombs to the Giant's Causeway, hexagonal patterns are prevalent in nature due to their efficiency. In a hexagonal grid each line is as short as it can possibly be if a large area is to be filled with the fewest hexagons. This means that honeycombs require less wax to construct and gain much strength under compression.


title: Hexagon

text: Irregular hexagons with parallel opposite edges are called parallelogons and can also tile the plane by translation. In three dimensions, hexagonal prisms with parallel opposite faces are called parallelohedrons and these can tessellate 3-space by translation.


title: Hexagon

text: In addition to the regular hexagon, which determines a unique tessellation of the plane, any irregular hexagon which satisfies the Conway criterion will tile the plane.


title: Hexagon

text: Pascal's theorem (also known as the "Hexagrammum Mysticum Theorem") states that if an arbitrary hexagon is inscribed in any conic section, and pairs of opposite sides are extended until they meet, the three intersection points will lie on a straight line, the "Pascal line" of that configuration.


title: Hexagon

text: The Lemoine hexagon is a cyclic hexagon (one inscribed in a circle) with vertices given by the six intersections of the edges of a triangle and the three lines that are parallel to the edges that pass through its symmedian point.


title: Hexagon

text: If the successive sides of a cyclic hexagon are "a", "b", "c", "d", "e", "f", then the three main diagonals intersect in a single point if and only if .


title: Hexagon

text: If, for each side of a cyclic hexagon, the adjacent sides are extended to their intersection, forming a triangle exterior to the given side, then the segments connecting the circumcenters of opposite triangles are concurrent.


title: Hexagon

text: If a hexagon has vertices on the circumcircle of an acute triangle at the six points (including three triangle vertices) where the extended altitudes of the triangle meet the circumcircle, then the area of the hexagon is twice the area of the triangle.


title: Hexagon

text: Let ABCDEF be a hexagon formed by six tangent lines of a conic section. Then Brianchon's theorem states that the three main diagonals AD, BE, and CF intersect at a single point.


title: Hexagon

text: In a hexagon that is tangential to a circle and that has consecutive sides "a", "b", "c", "d", "e", and "f",


title: Hexagon

text: If an equilateral triangle is constructed externally on each side of any hexagon, then the midpoints of the segments connecting the centroids of opposite triangles form another equilateral triangle.


title: Hexagon

text: A skew hexagon is a skew polygon with six vertices and edges but not existing on the same plane. The interior of such an hexagon is not generally defined. A "skew zig-zag hexagon" has vertices alternating between two parallel planes.


title: Hexagon

text: A regular skew hexagon is vertex-transitive with equal edge lengths. In three dimensions it will be a zig-zag skew hexagon and can be seen in the vertices and side edges of a triangular antiprism with the same D, [2,6] symmetry, order 12.


title: Hexagon

text: The cube and octahedron (same as triangular antiprism) have regular skew hexagons as petrie polygons.


title: Hexagon

text: The regular skew hexagon is the Petrie polygon for these higher dimensional regular, uniform and dual polyhedra and polytopes, shown in these skew orthogonal projections:


title: Hexagon

text: A "principal diagonal" of a hexagon is a diagonal which divides the hexagon into quadrilaterals. In any convex equilateral hexagon (one with all sides equal) with common side "a", there exists a principal diagonal "d" such that


title: Hexagon

text: There is no Platonic solid made of only regular hexagons, because the hexagons tessellate, not allowing the result to "fold up". The Archimedean solids with some hexagonal faces are the truncated tetrahedron, truncated octahedron, truncated icosahedron (of soccer ball and fullerene fame), truncated cuboctahedron and the truncated icosidodecahedron. These hexagons can be considered truncated triangles, with Coxeter diagrams of the form and .


title: Hexagon

text: There are other symmetry polyhedra with stretched or flattened hexagons, like these Goldberg polyhedron G(2,0):


title: Gigantism

text: Gigantism (, "gígas", "giant", plural γίγαντες, "gígantes"), also known as giantism, is a condition characterized by excessive growth and height significantly above average. In humans, this condition is caused by over-production of growth hormone in childhood, resulting in people up to in height.


title: Gigantism

text: It is a rare disorder resulting from increased levels of growth hormone before the fusion of the growth plate which usually occurs at some point soon after puberty. This increase is most often due to abnormal tumor growths on the pituitary gland. Gigantism should not be confused with acromegaly, the adult form of the disorder, characterized by somatic enlargement specifically in the extremities and face.


title: Gigantism

text: Gigantism is characterized by an excess of growth hormone (GH). The excess of growth hormone that brings about gigantism is virtually always caused by pituitary growths (adenomas). These adenomas are on the anterior pituitary gland. They can also cause overproduction of GH's hypothalamic precursor known as growth hormone releasing hormone (GHRH).