text:
Fall Colloq 2011
- 1 9/28 Chris Chafe, Ensembles, Basic Guidelines
- 2 10/5 Academic Guidelines, New Student Presentations, Dinner
- 3 10/12 Jonathan Berger and Christopher Willits
- 4 10/19 Andrea Agostini, Mark Applebaum
- 5 10/26 Edgar Berdahl, Computing Resources at CCRMA
- 6 11/02 Max Lab and Bay Area Prototyping Resources, Drupal, CMS, Craig Sapp and Eleanor Selfridge-Field , Ge Wang
- 7 11/09 Studios D and E, Digital Mixers, Marina Bosi
- 8 11/16 IPL/Studio C, Jaroslaw Kapuscinski, Jonathan Abel
- 9 11/30 Events and Concerts, Stage Use, Bruno Ruviaro, Tom Rossing
- 10 12/07 Listening Room, Fernando Lopez-Lezzcano, Julius Smith
9/28 Chris Chafe, Ensembles, Basic Guidelines
- Chris Chafe, Director of CCRMA
- Facilities Guidelines
- Ensembles
Email Forwarding: https://ccrma.stanford.edu/wiki/Email#Email_Forwarding
Password change: Type passwd in terminal
Web Directory: username/Library/Web ccrma.stanford.edu/~username
Backups: usr/ccrma/backup/username
CCRMA Room Booking: https://ccrma.stanford.edu/rooms/day.php
Stage Booking: http://music-calendar.stanford.edu/VirtualEms/
10/5 Academic Guidelines, New Student Presentations, Dinner
Academic Programs and Guidelines by Tricia Schroeter
New students have 5 minutes to introduce themselves the CCRMA Community and talk about the type of research and creating they have done or are interested in doing. Delicious dinner from Mediterranean Wraps ($5 donation requested).
10/12 Jonathan Berger and Christopher Willits
Jonathan Berger's orchestral, chamber, vocal and electroacoustic works have been performed throughout the world. Miracles and Mud, Berger's recent Naxos recording of music for solo violin and string quartet has received considerable critical acclaim. Berger's recent commissions include The Bridal Canopy (Berger's fourth string quartet, composed for the St. Lawrence String Quartet and commissioned by the Friends of Chamber Music, Denver), Tears In Your Hand (Commissioned by Chamber Music Toronto for the Gryphon Trio), and Of Hammered Gold (Commissioned by Chamber Music America). Major past commissions include the National Endowment for the Arts, The Rockefeller Foundation, WDR, the Bourges Festival and the Mellon Fund. Current commissions include works for Ensmble Meitar, Trio Voce, violist Gilad Karmi, and Fulcrum Point. Berger's works are available on Naxos, Sony, Neuma, CRI and Harmonia Mundi. In addition to composition Berger is an active researcher with over 60 publications in a wide range of fields relating to music, science and technology. Berger is The Denning Family Provostial Professor at Stanford and Co-Director of the Stanford Institute for Creativity and the Arts (SICA) and the University's arts initiative.
Christopher Willits is an artist- a musician, guitarist, producer, photographer, filmmaker all-in-one. Willits occupies a unique corner of the electronic-art-music universe—hovering above the intersection of electronic production's nuts and bolts, new media art, and a wide-open creative mind. "i am a conduit of the process, a kind of gardener," he says. "I simply imagine, intuit, respond and do the work laid before me." Willits' tireless responding and doing and working has produced 20 albums in 10 years—solo and in collaboration with artists including Ryuichi Sakamoto, Matmos, Zach Hill, and Taylor Deupree—and an organic, multi-faceted sound that expands like the vines of an electro-acoustic kudzu plant. Christopher Willits is a teacher, a label owner (the experimental hub Overlap.org), a meditator, a tech geek, a visual/new media artist, and virtuosic musician in one. In other words, there's no one out there quite like him. Willits designs much of his own software, and his music is a holistic universe in which all elements are interconnected; he folds his guitar lines into bleary, unrecognizable shapes and polyrhythmic textures, adding strokes of percussion, horns, and his own voice until the whole glows with an earthly inner light. A full list of Christopher Willits' releases and accomplishments would take up considerable column space, but a beginner's guide to Willits includes 2002's Folding, and the Tea (his watery 12k debut), 2006's landmark Surf Boundaries (his first full-length record on Ghostly International), 2008's Ocean Fire (Willits' collaboration with renowned pianist / composer Ryuichi Sakamoto), and 2009's Live on Earth Vols. 1 & 2 (a pair of self-released live albums dedicated to his fans and supporters).
Willits has been instrumental in redefining the guitar in the digital age. Using custom-built software, Willits morphs melodic guitar loops and photo/video experiments into folded rhythms of harmony, memory, color and texture. Named "the center cell of a complex indie rock-avant-garde-electronic art Venn diagram in the Bay Area" (San Francisco Bay Guardian), and "The Picasso of Sound" (Tokafi Magazine), Willits defies genre distinctions while still defining a sound and style of his own. His guitar lines fold and weave into each other creating complex patterns of interlocking rhythm, melody, and texture.
Every project sees him evolving and expanding his creative vision. In addition to his solo work, Willits has created a vast range of music collaborations, sound installations, and film/video projects. His band project Flossin involves Zach Hill, Kid606, and Matmos, The North Valley Subconscious Orchestra is Willits and Brad Laner, formerly of Medicine. Other frequent collaborators include Scott Pagano, Taylor Deupree, and Ryuichi Sakamoto. Willits' numerous releases and collaborative projects cover a broad spectrum of musical styles, and include one main commonality: Willits' love of pattern and his unique approach to the guitar and sound + light. Willits completed his Master's Degree in Electronic Music at Mills College where he studied with Pauline Oliveros and Fred Frith. At Mills he explored structure-generating processes in music; a focus not unfamiliar to former Mills affiliates John Cage and Steve Reich. Prior to Mills, Willits focused on painting, video art, sound art and music at the Kansas City Art Institute. In addition to all of this, Willits is the Founder / Director of the experimental media label Overlap.org .
10/19 Andrea Agostini, Mark Applebaum
Andrea Agostini, born in 1975, starts as a young boy his music studies. He obtains honors degree both in composition and electronic music, followed soon by a piano degree. He has attended Master Classes with, among others, Alessandro Solbiati, Ivan Fedele, Brian Ferneyhough, Michel Jarrel, François Paris. His works have been selected and award-winning in several international competitions such as Prix Noroit 2002, Musica Viva 2003, 3rd Seul Competition for Composers, Gaudeamus Music Week 2005. He's written for radio, cinema, and theatre. His compositions have been publicly performed in Italy and abroad: American Music Week 2002 in Sofia, Sincronie Festival (Milan) 2004 and 2005, Istituto Italiano di Cultura, WDR Köln, Festival Bourges 2006, Festival Spark 2007 (Minneapolis), Saison Musical 2006 and 2007 Abbay Royaumont.
Mark Applebaum is associate professor of composition at Stanford University. He received his Ph.D. in composition from the University of California, San Diego where he studied with Brian Ferneyhough. His solo, chamber, choral, orchestral, operatic, and electroacoustic music has been performed throughout the United States, Europe, Africa, and Asia with notable premieres at the Darmstadt sessions. He has received commissions from the Merce Cunningham Dance Company, the Fromm Foundation, and the Vienna Modern Festival, among others. Applebaum builds electroacoustic sound-sculptures and is active as a jazz pianist. His music can be heard on the Innova, Tzadik, Capstone, Everglade, and SEAMUS labels. See also: www.markapplebaum.com.
10/26 Edgar Berdahl, Computing Resources at CCRMA
Edgar Berdahl is a lecturer in the Music Department at Stanford University in California, USA. Prior to receiving his PhD from Stanford, Berdahl earned a BS in Electrical Engineering and Computer Science at UC Berkeley. His research interests include physical modeling, human-computer interaction, robotics, signal processing, and sound synthesis. He seeks to enhance "digital" musical interactions so that they "seem more analog."
Computing at CCRMA
- CCRMA Wiki editing [1]
- Interesting places on the CCRMA network:
- User directories
- Other useful network mounts
- Local partitions on CCRMA hosts
/zap, /scratch, /audio
- CCRMA Net
- The Departmental Firewall and creative network ports, plan ahead.
- Default shell: currently
tcsh. Can change to
bashor other shell. Contact Sys Admins.
- Unix: command line practice lab:
ssh, slogin
- w
- mkdir -p
- ls, ll, l.
- cp, scp
- mv
- wget
- du -sh
- df -h | grep [explain pipe and > text redirect]
- ps -e | grep
- top
- mount/umount
- chmod, chown, chgrp
- ping
- finger
- fortune
11/02 Max Lab and Bay Area Prototyping Resources, Drupal, CMS, Craig Sapp and Eleanor Selfridge-Field , Ge Wang
Technical Topic: We will talk about the CCRMA web page built on the Drupal content management system.
We will go over the resources available to you in the Max Lab and the various prototyping facilities at Stanford (PRL, Sculpture studio) and the general Bay Area Community (Tech Shop, Community College Classes, Crucible, Online Prototyping)
Important CCRMA Webpage links:
Create an account - Log in, click on "My Account" Post events/talks at CCRMA - Create Content > Event Post your papers - https://ccrma.stanford.edu/papers Post job announcements - https://ccrma.stanford.edu/classifieds/jobs
Bay Area Prototyping Resources: https://ccrma.stanford.edu/wiki/Prototyping
CCARH - Craig Sapp and Eleanor Selfridge-Field
The music information lab in the Braun Music Center (#129-130) works in intersecting areas of music, music theory, computer science, and cognitive studies. Symbolic music representation systems (http://www.ccarh.org/publications/books/beyondmidi) are central to all of these endeavors.
Specific areas of activity include:
1. Robust encoding, acquisition, and printing systems across platforms (Score, Finale, Sibelius, MuseScore, Noteflight, MuseData, OCR, et al: see http://253.ccarh.org)
2. Symbolic music retrieval via the Themefinder database (for low- and high-precision searches of encoded music): see http://www.themefinder.org/
3. Music analysis and tool development for the Humdrum Toolkit (http://humdrum.ccarh.org/)
4. Methods of visualization, such as [WINDOWS-1252?]Sapp's keyscapes (structural harmonic analyses): http:// ccrma.stanford.edu/~craig/keyscape/class
5. Data interchange and the re-purposing of musical [WINDOWS-1252?]data—
MusicXML: http://recordare.com/musicxml/specification/ MEI: http://www2.lib.virginia.edu/innovation/mei/
We also build aggregations of encoded data for notation and analysis. Our major collections are these:
1. MuseData: http://www.musedata.org 2. KernScores: http://kern.humdrum.net
Courses offered at CCARH include
1. Music 252 Introduction to Music Notation Software (autumn) 2. Music 253 Introduction to Musical Information (winter) 3. Music 254 Music Query, Analysis, and Style Simulation (spring): project-oriented course
For an aggregation of all these projects, see the Center for Computer Assisted Research in the Humanities: http://www.ccarh.org
Ge Wang is an Assistant Professor at Stanford University's Center for Computer Research in Music and Acoustics (CCRMA), and researches interactive software systems for computer music, programming languages, social/mobile music, and education at the intersection of computer science and music. Ge is the author of the ChucK audio programming language, the founding director of the Stanford Laptop Orchestra (SLOrk), and the co-founder and director of the Stanford Mobile Phone Orchestra (MoPhO). Ge is also the Co-founder, CTO, and Chief Creative Officer of Smule, and the designer of the iPhone's Ocarina and the iPad's Magic Piano.
11/09 Studios D and E, Digital Mixers, Marina Bosi
Technical Topic: Hands on instruction and practice using the Yamaha digital mixers available in Studios C, D, E and the CCRMA Stage. Discussion of the software and hardware tools available in Studios D and E.
Marina Bosi is Consulting Professor in the Music Department at Stanford University and is also a founding member and director of the Digital Media Project, a non-profit organization that promotes successful development, deployment, and use of Digital Media. Previously, Dr. Bosi was Chief Technology Officer of MPEG LA®, a firm specializing in the licensing of multimedia technology; VP-Technology, Standards and Strategies at Digital Theater Systems (DTS); and was part of the research team at Dolby Laboratories working on AC-2 and AC-3 technology where she also led the MPEG-2 AAC development. Dr. Bosi has been actively involved in the development of standards for audio and video coding and for managing digital content, contributing to the work of ANSI, ATSC, DVD Forum, DVB, ISO/IEC MPEG, SDMI, and SMPTE.
A past President of the Audio Engineering Society (AES), Dr. Bosi also served the AES in various capacities including as a member of the Board of Governors and as VP of the Western Region USA and Canada. Dr. Bosi is a member the Technical Committee on Audio and Electroacoustics of the IEEE Signal Processing Society, a senior member of IEEE, and a member of ASA. Dr. Bosi received the AES Fellowship Award for her contributions to the standardization of audio coding, video coding, and secure digital content. She received the AES Board of Governors Award twice: for her co- chairmanship of the 96th AES Convention and again for her co-chairmanship of the 17th AES International Conference, the first scientific international conference dedicated to the topic of high quality audio coding. Dr. Bosi was the editor of MPEG-2 Advanced Audio Coding (AAC) for which she received a Certificate of Appreciation from ISO/IEC. She also has received several awards for her scholarship from both the French and Italian governments. Dr. Bosi holds several patents and publications in the field and is author of the acclaimed textbook "Introduction to Digital Audio Coding and Standards" (Kluwer/Springer December 2002) translated into Chinese and Korean.
11/16 IPL/Studio C, Jaroslaw Kapuscinski, Jonathan Abel
Technical Topic: Hands on instruction and practice using the Yamaha digital mixers available in Studios C, D, E and the CCRMA Stage Jarek will give a tour of Studio C (IPL). https://ccrma.stanford.edu/wiki/CCRMA_IPL_Studio_C_User_Guide
Jaroslaw Kapuscinski is an intermedia composer and pianist whose work has been presented at New York's MOMA, Zentrum für Kunst und Medientechnologie in Karlsruhe, Museum of Modern Art Palais de Tokyo in Paris, National Reina Sofia Museum in Madrid and many other venues. He has received numerous awards among else at the UNESCO Film sur l'Art Festival in Paris in 1992, VideoArt Festival in Locarno in 1992 and 1993, Manifestation Internationale Vidéo et Art Éléctronique in Montréal in 1993 and International Festival of New Cinema and New Media in Montréal in 2000. Kapuscinski's primary interest is creation and performance of works, in which musical instruments are used to control multimedia content. He was first trained as a classical pianist and composer at the Chopin Academy of Music in Warsaw and expanded into multimedia at a residency at Banff Centre for the Arts in Canada (1988) and during doctoral studies at the University of California, San Diego (1992-1997). Kapuscinski is actively involved in intermedia education. As of 2008 he is Assistant Professor of Composition and Director of Intermedia Performance Lab at Stanford University. He has taught at McGill University in Montreal, Royal Academy of Arts and Music in the Hague, Art Conservatory and Music Academy in Odense, Conservatory of Music at University of the Pacific and lectured internationally. He has published among else "Composing with Sounds and Images", an article outlining his intermedia theory.
Jonathan S. Abel is a consulting professor at the Center for Computer Research in Music and Acoustics (CCRMA) in the Music Department at Stanford University where his research interests include audio and music applications of signal and array processing, parameter estimation, and acoustics. From 1999 to 2007, Abel was a co-founder and chief technology officer of the Grammy Award-winning Universal Audio, Inc. He was a researcher at NASA/Ames Research Center, exploring topics in room acoustics and spatial hearing on a grant through the San Jose State University Foundation. Abel was also chief scientist of Crystal River Engineering, Inc., where he developed their positional audio technology, and a lecturer in the Department of Electrical Engineering at Yale University. As an industry consultant, Abel has worked with Apple, FDNY, LSI Logic, NRL, SAIC and Sennheiser, on projects in professional audio, GPS, medical imaging, passive sonar and fire department resource allocation. He holds Ph.D. and M.S. degrees from Stanford University, and an S.B. from MIT, all in electrical engineering. Abel is a Fellow of the Audio Engineering Society.
11/30 Events and Concerts, Stage Use, Bruno Ruviaro, Tom Rossing
Technical Topic: We will go over how to book events and concerts at CCRMA including scheduling, publicity, and gear check-out. We will also do a hands on demo of the major components of the stage including the mixing board and the lighting board.
Bruno Ruviaro is a composer originally from São Paulo, Brazil, and has been living in the United States since 2002. He composes both acoustic and electronic music. Recordings of his two most recent pieces ("Intellectual Impropriety 0.6", for laptop orchestra, and "Drei, Dai, Dry", for viola, cello, and percussion), can be heard at <http://www.brunoruviaro.com/ >. Current interests include the study and criticism of intellectual property and musical borrowing in both classical and popular music history. He is currently a Post-Doctoral Scholar and concert organizer at the Center for Computer Research in Music and Acoustics (CCRMA), Stanford University.
Thomas D. Rossing (Distinguished Research Professor of Physics Emeritus, Northern Illinois University and Visiting Professor of Music at Stanford University) is the author of over 400 publications, including 18 books, mostly on magnetism and acoustics. His latest books are the Springer Handbook of Acoustics and The Science of String Instruments, which is currently in press at Springer. He is also writing a chapter for the 3rd edition of The Psychology of Music by Diana Deutsch. He has directed church choirs and handbell choirs, played clarinet in orchestras and chamber ensembles, and appeared as tenor soloist. He has been a visiting professor at universities in Korea and Scotland as well as in the United States.
He is a Fellow of the American Physical Society, The Acoustical Society of America, the American Association for the Advancement of Science, and IEEE. He was awarded the Silver Medal in Musical Acoustics and the Gold Medal in Acoustics by the Acoustical Society of America and the Robert Millikan Medal by the American Association of Physics Teachers. He will receive the Rayleigh Medal from the Mexican Institute of Acoustics in November. His biography appears in Who's Who in America and in the New Groves Dictionary of Music and Musicians.
12/07 Listening Room, Fernando Lopez-Lezzcano, Julius Smith
Technical Topic: Nando will give a tour of the listening room. Information about the rooms can be found here: https://ccrma.stanford.edu/wiki/Listening_Room_Specs https://ccrma.stanford.edu/room-guides/listening-room
Fernando Lopez-Lezcano is a composer, performer, lecturer and computer systems administrator at CCRMA, Stanford University. He has been teaching and taking care of computing resources there since 1993, and created and maintains since 2001 the Planet CCRMA collection of open source sound and music packages for Linux. He has been involved in the field of electronic music since 1976 as a composer, instrument builder and performer, blurring the lines of his dual background in music (piano and composition) and electronic engineering. His music has been released on CD and played in the Americas, Europe and East Asia. He was the "Edgar Varese Guest Professor" at TU Berlin during the Summer 2008 semester.
Julius O. Smith teaches Music 420 (Signal Processing Models in Musical Acoustics) and 421 (Audio Applications of the Fast Fourier Transform) and supervises related research at CCRMA. He is formally a professor of music and associate professor (by courtesy) of electrical engineering. In 1975, he received his BS/EE degree from Rice University, where he got started in the field of digital signal processing and modeling for control. In 1983, he received the PhD/EE degree from Stanford University, specializing in techniques for digital filter design and system identification, with application to violin modeling. His work history includes the Signal Processing Department at Electromagnetic Systems Laboratories, Inc., working on systems for digital communications, the Adaptive Systems Department at Systems Control Technology, Inc., working on research problems in adaptive filtering and spectral estimation, and NeXT Computer, Inc., where he was responsible for sound, music, and signal processing software for the NeXT computer workstation. Prof. Smith is a Fellow of the Audio Engineering Society and the Acoustical Society of America. He is the author of four online books and numerous research publications in his field. For more information, see http://ccrma.stanford.edu/~jos/.


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We're sorry, but this item is no longer for sale. However, there may be more New & Pre-Owned Apple items available.
Our selection of available New & Pre-Owned Macs is constantly changing. We highlight many of the best deals on our Specials Page, or you can view our full inventory of new, refurbished and OWC certified systems.
Apple 27-inch iMac
(Mid 2011)
Model ID: iMac12,2 View how to find model ID
This Mac comes pre-installed with Mac OS 10.12.5 Sierra (or later) and supports operating system version 10.6.6 Snow Leopard through 10.13.6 High Sierra.
Internal Storage
Internal Optical
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*While researched thoroughly via independent resources, OWC does not make any claim to accuracy or completeness of these specifications.
AirMac®, AirPlay®, AirPort®, AirPort Express®, AirPort Extreme®, AirTunes®, A.Pack®, Aperture®, Apple®, AppleCAT®, AppleCD SC®, Apple Cinema Display®, AppleScript®, AppleScript Studio®, AppleShare®, AppleTalk®, Apple TV®, AppleWorks®, Aqua®, Back to My Mac®, Bonjour®, Boot Camp®, Carbon®, Claris®, Cocoa®, Cocoa Touch®, ColorSync®, Cover Flow®, Dashcode®, DVD Studio Pro®, EdView®, Web portal eMac®, Encyclomedia®, EtherTalk®, Exposé®, FaceTime®, FairPlay®, FileVault®, Final Cut®, Final Cut Pro®, Final Cut Studio®, Finder®, FireWire®, FireWire symbol®, FontSync®, GarageBand®, HyperCard®, HyperTalk®, iBook®, iBooks®, iCal®, iChat®, iDVD®, iLife®, iMac®, ImageWriter®, iMovie®, Inkwell®, Instruments®, Inter·Poll®, iPad®, iPhone®, iPhoto®, iPod®, iPod classic®, iPod Hi-Fi®, iPod nano®, iPod shuffle®, iPod Socks®, iPod touch®, iSight®, iTunes®, iTunes Logo®, iTunes Pass®, iWork®, Jam Pack®, Keychain®, Keynote®, Leopard®, LiveType®, LocalTalk®, Logic®, Logic Studio®, Mac®, Mac logo®, MacApp®, MacBook®, MacBook Air®, MacDNS®, Macintosh®, Mac OS®, Mac Pro®, MacTCP®, MagSafe®, MainStage®, MPW®, Numbers®, Objective-C®, OpenPlay®, OS X®, Pages®, Panther®, Photo Booth®, Pixlet®, Podcast Logo®, PowerBook®, Power Mac®, Quartz®, QuickDraw®, QuickTime®, QuickTime logo®, Rosetta®, SADE®, Safari®, Shake®, Sherlock®, Snow Leopard®, Soundtrack®, Spaces®, Spotlight®, SuperDrive®, Think different®, Tiger®, Time Capsule®, Time Machine®, TrueType®, Tubes®, Ultrabeat®, Velocity Engine®, WaveBurner®, WebObjects®, Works with iPhone logo®, Xcode®, Xgrid®, Xsan®, and Xserve® are trademarks of Apple Inc., registered in the U.S. and other countries.
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Intel, Intel Core, and Xeon are trademarks of Intel Corporation in the U.S. and/or other countries.


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Modern Elliptic Curve Factorization, Part 1
April 23, 2010
We discussed Hendrik Lenstra's algorithm for factoring integers using elliptic curves in three previous exercises. After Lenstra published his algorithm in 1987, mathematicians studied the algorithm extensively and made many improvements. In this exercise, and the next, we will study a two-stage version of elliptic curve factorization that features improved elliptic arithmetic and is much faster than Lenstra's original algorithm. Today's exercise looks at the improved elliptic arithmetic; we will look at the two-stage algorithm in the next exercise.
If you look at Lenstra's original algorithm, much of the time is spent calculating modular inverses. Peter Montgomery worked out a way to eliminate the modular inverses by changing the elliptic arithmetic; instead of using the curve y2 = x3 + ax + b, Montgomery uses the curve y2 = x3 + ax2 + x. Additionally, he does a co-ordinate transform to eliminate the y variable, so we don't need to figure out which of the quadratic roots to follow. Finally, Montgomery stores the numerator and denominator of the a parameter separately, eliminating the modular inverse. We won't give more of the math; for those who are interested, a good reference is Prime Numbers: A Computational Perspective by Richard Crandall and Carl Pomerance.
Here are the elliptic addition, doubling and multiplication rules for Montgomery's elliptic curves:
A curve is given by the formula y2 = x3 + (An / Ad – 2)x2 + x (mod n).
A point is stored as a two-tuple containing its x and z co-ordinates.
To add two points P1(x1,z1) and P2(x2,z2), given the point P0(x0,z0) = P1 – P2 (notice that the curve is not used in the calculation):
x = ((x1–z1) × (x2+z2) + (x1+z1) × (x2–z2))2 × z0 mod n
z = ((x1–z1) × (x2+z2) – (x1+z1) × (x2–z2))2 × x0 mod n
To double the point P:
x = (x+z)2 × (x–z)2 × 4 × Ad mod n
z = (4 × Ad × (x–z)2 + t × An) × t mod n where t = (x+z)2 – (x–z)2
Multiplication is done by an adding/doubling ladder, similar to the method used in the Lucas chain in the exercise on the Baillie-Wagstaff primality checker; the Lucas chain is needed so that we always have the point P1–P2. For instance, the product 13P is done by the following ladder:
2P = double(P)
3P = add(2P, P, P)
4P = double(2P)
6P = double(3P)
7P = add(4P, 3P, P)
13P = add(7P, 6P, P)
Richard Brent gave a method to find a suitable elliptic curve and a point on the curve given an initial seed s on the half-open range [6, n), with all operations done modulo n:
u = s2 – 5
v = 4s
An = (v–u)3 (3u+v)
Ad = 4u3v
P = (u3, v3)
Your task today is to write the three functions that add, double, and multiply points on an elliptic curve and the function that finds a curve and a point on the curve; the payoff will be in the next exercise that presents elliptic curve factorization. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.
5 Responses to "Modern Elliptic Curve Factorization, Part 1"
April 23, 2010 at 12:35 PM
[…] today's Programming Praxis exercise we have to implement an algorithm for curve factorization. The Scheme […]
April 25, 2010 at 8:23 PM
Python version.
def init( n, seed ): u = ( seed*seed - 5 ) % n v = 4*seed % n num = pow(v-u, 3, n) * (3*u + v) % n den = 4 * pow(u,3,n) * v % n A = num, den P = (pow(u, 3, n), pow( v, 3, n) ) return A, P def add( p1, p2, p0, n ): x1,z1 = p1 x2,z2 = p2 x0,z0 = p0 t1 = (x1-z1)*(x2+z2) t2 = (x1+z1)*(x2-z2) newx = z0 * pow( t1 + t2, 2, n ) % n newz = x0 * pow( t1 - t2, 2, n ) % n return newx, newz def double( p, A, n ): x,z = p An, Ad = A t1 = pow(x + z, 2, n) t2 = pow(x - z, 2, n) t = t1 - t2 newx = t1 * t2 * 4 * Ad % n newz = (4 * Ad * t2 + t * An) * t % n return newx, newz def multiply( m, p, A, n ): if m == 0: return 0,0 elif m == 1: return p else: q = double( p, A, n ) if m == 2: return q b = 1 while b < m: b <<= 1 b >>= 2 r = p while b: if m&b: q, r = double(q, A, n), add(q, r, p, n) else: q, r = add(r, q, p, n), double(r, A, n) b >>= 1 return r n,s = 5569379,4921134 A, P1 = init(n, s) P2 = double(P1,A,n) P3 = add(P2,P1,P1,n) P4 = double(P2, A, n) P6 = double(P3, A, n) P7 = add(P4,P3,P1,n) P13 = add(P6,P7,P1,n) P13a = multiply(13,P1,A,n) print P13, P13a, P13 == P13a
January 18, 2011 at 12:24 PM
Hi Programmingpraxis
Could you tell me if my implementation is correct or not specially for multiPoint function as i was trying to reduce one more call of mulitpOint function.
--y^2 = x^3+ax^2+b data Elliptic = Conelliptic Integer Integer Integer deriving (Eq,Show) data Point = Conpoint Integer Integer deriving (Eq,Show) addPoints::Point->Point->Point->Integer->Point addPoints (Conpoint x_1 z_1) (Conpoint x_2 z_2) (Conpoint x_0 z_0) n = let x_3= mod ((((x_1-z_1)*(x_2+z_2)+(x_1+z_1)*(x_2-z_2))^2)*z_0) n z_3= mod ((((x_1-z_1)*(x_2+z_2)-(x_1+z_1)*(x_2-z_2))^2)*x_0) n in (Conpoint x_3 z_3) doublePoint::Point->Elliptic->Point doublePoint (Conpoint x z) (Conelliptic an ad n) = (Conpoint (mod x' n) (mod y' n)) where x'= mod (4*ad*(x+z)^2*(x-z)^2) n y'= mod ((4*ad*(x-z)^2+t*an)*t) n where t=(x+z)^2-(x-z)^2 multiPoint::Integer->Integer->Point->Elliptic->Point multiPoint _ 0 _ _ = (Conpoint 0 0) multiPoint _ 1 pOint _ = pOint multiPoint n k pOint eCurve =let p=multiPoint n (div k 2) pOint eCurve in case even k of True -> doublePoint p eCurve _ -> addPoints p (addPoints p pOint pOint n) pOint n -- for 7p i am using 6p+pOint montgomeryCurve::Integer->Integer->[Integer] montgomeryCurve s n = let u=mod (s*s-5) n v=mod (4*s) n an=mod (((v-u)^3)*(3*u+v)) n ad=mod (4*u^3*v) n in [an,ad,n,mod (u*u*u) n,mod (v*v*v) n]
January 21, 2011 at 10:07 PM
[…] previous example except using Montgomery curve rather than Lenstra curve. Programmingpraxis used Montgomery curve to find the prime factorisation. I personally feel that Lenstra algorithm worked fine when […]


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BV to host Foreign Language Fair
Staff Writer
Star Courier
Bureau Valley High School will host its annual Foreign Language Fair on Thursday, Feb. 28 featuring food and entertainment.
Mexican and German buffets will serve from 5:30 to 7:30 p.m. in the commons area and feature tacos, chicken fajitas, brats, hot dogs and goulash.
Designed to be a family-friendly event, young children can enjoy the "It's a Small World" parade and the free craft tables.
Spanish and German Club members will perform songs and dances.
Meals start at $4 and students get in free.
Adults pay a $1 admission.


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Why apply for Washington Title Loans?
Most Americans face financial difficulties at least a few times in their lives. Unfortunately, we can neither predict nor prevent accidents, illness or death. Moreover, any emergency situation leads to extra costs. However, many people do not have additional funds to cover unexpected expenses. Financial hardships also affect our lives as we may not be able to pay bills and household expenses. Of course, you can always borrow money from family and friends, or go to the bank for a loan. However, friends and family often have their own problems. The banks will only give you a loan if you have good credit history. However, is there a way out for people with bad credit history? Of course! If you own a car and you are a title holder, you can apply for a Title Loan in Washington, NJ.
Title loan in Washington, NJ. How does it work?
A Title Loan is a secured loan that uses the value of your car as collateral and gives you the opportunity to get money to solve all your difficulties. If you have been turned down by banks or credit unions, you can get your Title Loan in Washington, NJ today.
In order to get a Title Loan in Washington, NJ, you need to fill out an application form. Many people are looking for a lender near me in Washington, NJ because they believe this is the fastest way to get approved. However, in fact, in order to get a loan as quickly as possible, you need to fill out an online form on the lender's website. It is not only fast, but also convenient! If you are worried about the safety of your data, then you should know that when you submit an application on the site, your data is encrypted. Thus, your personal information is protected and cannot be transferred to third parties. When filling out the application in Washington, NJ, you need to provide your data and information about your vehicle. After sending the data, the lender will review your information and contact you on the same day!
Next, you need to bring the car and its title to the lender's store for a cost estimate in Washington, NJ. The specialist takes into account factors such as the cost of the car and its make, as well as age, mileage, and more. The absence of accidents will also be an advantage. Thus, the more expensive your car is, the more you can get. After evaluating the vehicle, you will be offered the amount you can receive. Thus, if you are approved, you can sign a contract and receive a payment.
It is important to understand that the title of your car will be transferred to the lender at the time the loan is paid in Washington, NJ. Thus, your car is the collateral, and the lender is the temporary owner of your title. In order not to lose your car, it is necessary to pay off the entire loan amount with interest on time. The terms and conditions of payment in Washington, NJ will be specified in the contract. Also, before signing the contract, you can discuss all the questions with the lender directly.
How much can I get with a Title Loan in Washington, NJ?
Of course, the main question for every borrower is "how much can I get with a Title Loan in Washington, NJ?" As known, the loan amount depends on the value and condition of the car, as well as on your salary and creditworthiness. Lenders in Washington, NJ offer loans up to the full cost of your car, however, you can usually get from 25 to 50 percent. You should not expect that you will receive the full cost of your car, as this requires you to have a practically new car in perfect condition.
Most borrowers in Washington, NJ receive an amount between $ 1,000 and $ 5,000. However, if you are applying for a larger loan, it will be better to compare the offers of different lenders. This way, you can find a lender who will offer you up to $ 10,000.
What are Title loan repayment terms in Washington, NJ?
The Title Loan repayment terms in Washington, NJ directly depend on the loan amount. As a rule, the larger the loan, the longer the repayment period. So, the terms vary from 1 to 3 years in Washington, NJ. However, it is worth remembering that the longer the term of your Title Loan is, the more interest you will pay on the loan. Thus, it will be beneficial for you to take a small loan and cover it quickly in order not to overpay the interest rate.
Title Loan Approval Time in Washington, NJ
If you are in an emergency and urgently need money, every day can be crucial for you. However, don't worry because a Title Loan in Washington, NJ gives you the opportunity to be approved on the same day you apply. Moreover, in some cases, you can receive payment on the day of application and solve your financial problems.
Title Loan for Bad Credit in Washington, NJ
You can get a Title Loan even if your credit history is not a role model. The main criterion for the approval of your application is a regular source of income.
However, it should be understood that a Title loan in Washington, NJ has high interest rates. So, if you have bad credit, you can get incredibly high and unfavorable interest rates. Compare offers from different lenders before making a decision.
Eligibility criteria for a title loan in Washington, NJ
In order to obtain a Title Loan in Washington, NJ, you need to meet certain lender requirements. Read the basics before applying.
- be at least 18 years old
- have a government-issued ID
- have a source of income
- have a permanent residence address
- provide a contact phone number and email
- provide original car name
- provide insurance and vehicle registration
- provide a title
Best Car Title Loan places in Washington, NJ:
Unfortunately, no Title Loans store addresses have been found. Try to apply for the necessary cash advance online.


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Even when I lived outside of the US, whether in Uruguay, Israel, etc., I'd hear about Southern cooking. When I first came to the States in 1962 and moved to Richmond, VA (the capital of the Confederacy), I actually got to taste a few superb kosher variations on the Southern theme.
Recently, I came across Simply Southern – With a Dash of Kosher Soul, a cookbook published by the Margolin Hebrew Academy/Feinstone Yeshiva of the South of Memphis, TN. I couldn't wait to try out some of the book's delicacies, I wasn't disappointed! The recipes are a easy to make, short-cutting more complex directions with readily available ingredients that make preparation a snap. This ain't no diet cookbook, so if you've been watching your waist after yom tov feasting save this for the times when you want to cook quick tasty dishes with that special touch of true Americana. The recipes are clear, the assortment fun, pretty to look at and absolutely delicious.
For the last week we made quite a few of them and each proved delectable. The recipes are divided into ten sections running from
- Appetizers and Starters
- Soups and Sandwiches
- Salads
- Brunch & Dairy
- Pasta, grains & Rice
- Meats
- Poultry
- Fish
- Vegetables & Side Dishes
- Desserts
As you can see, it covers the gamut of the most common cooking types. It is hard to chose just one recipe to share, in fact it's hard to chose, two, three or even four favorites from those we tried. But here are two very Southern selections:
Real Fried Chicken
True Southerners make enough for leftovers. Nothing beats cold fried chicken for lunch the day after. Do not skip the salt! salt is an especially important ingredient to the authentic taste of this signature dish of Dixie!
1 quart water
2 tablespoons salt
2 tablespoons cayenne pepper
2 teaspoons garlic powder
1 1/2 teaspoons white pepper
1 tablespoon soy sauce
2 teaspoons Worcestershire sauce
Whisk together water, salt, cayenne, garlic powder, white pepper, soy sauce, and Worcestershire sauce.
4 cut up chickens
12 cups vegetable oil
Self rising flour
2 eggs, beaten
2 tablespoons water
3 cups all-purpose flour
1 tablespoon salt
1 teaspoon garlic powder
1 teaspoon cayenne pepper
1 teaspoon white pepper
Add chicken pieces to marinade. Toss to coat. Cover and refrigerate for 24 hours.
Heat oil in a deep fryer to 360-375 degrees. Drain marinade from chicken on paper towels and pat dry. Sprinkle chicken on both sides with self-rising flour. Blend eggs and water. Combine all-purpose flour, salt, garlic powder, cayenne and white pepper. Dip chicken in egg wash. Dredge in flour mixture. Place chicken on a large baking sheet. Let sand for 10 minutes. Fry chicken in hot oil turning a few times for 20-25 minutes or until golden browned. Drain on a rack over paper towels.
For dessert I loved the Chess Pie, I also liked the humor in the intro to this dish.
Chocolate Chess Pie
Chess pie is one of the South's great contributions to the culinary arts. One folk story asserts that it was originally called "just pie," which was drawled as "jus' pie," eventually rolling off the tongue as "chess pie." This is always a favorite!
1 1/4 cups sugar
1/4 cup unsweetened cocoa powder
4 tablespoons margarine, melted
2 eggs
10 tablespoons soymilk
1 1/2 teaspoons vanilla
1/8 teaspoon salt
1 (9-inch) pie shell, unbaked
1 (8-ounce) container frozen whipped topping, thawed
Chocolate syrup
Preheat oven to 350 degrees. Combine sugar, cocoa, and margarine in a bowl. Add eggs and beat until smooth. Blend in soymilk, vanilla and salt. Pour filling into pie shell. Bake at 350 degrees for 45 minutes until tester comes out clean. Cool top with whipped topping. Pie freezes well. Drizzle chocolate syrup across the top!
Each section starts out with a few short paragraphs detailing the transition of Southern cooking into Kosher cooking or an occasional anecdote to bring the Memphis community a little closer to wherever you are. Liberally sprinkled with humor and folksy story tellin' Simply Southern – With a Dash of Kosher Soul is sure to change your view of classic American cooking.
Enjoy it, gentle reader, enjoy it in all its finger lickin' goodness!


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A Wednesday – Movie review
While I was in a cinema theatre watching a movie about terrorism, five blasts took place in Delhi…between 6:15 PM and 7 PM.
A Wednesday is the movie I saw earlier this evening…and it was about terrorism. It was about how a terrorist holds a whole city to hostage by planting five bombs in the city. One comes out of the cinema hall feeling vindicated at the ending…even satisfied. Even though one knows that it is not quite right to feel this way. A feeling that (briefly) intensified for me as soon as I heard about the bomb blasts in Delhi…
Well, I wish I could tell the whole story right here, but it will ruin the movie for those who haven't seen it…this is a movie that one enjoys best if one doesn't know the ending.
There have been several movies about terrorism in the recent past…and when I saw A Wednesday I couldn't help but compare it to Amir. But three things make A Wednesday glaringly different:
1) A Wednesday has an original script.
2) It has no protagonist.
3) It has a happy ending.
I am a sucker for thrillers and for happy endings and I guess that is why I liked this movie even though happy endings are not always what we see in real life…
What is A Wednesday exactly about? (no spoilers)
The story is a simple one. There are bombs, five of them…and this we find that out pretty early on in the movie. One bomb is planted at the police station itself…and as for the other bombs, well that is for the police to find out. And as is common with all terrorists, the person who has planted the bombs wants something in exchange…
There is suspense even though we know that the police commissioner (Prakash Rathod, who is the narrator) is alive and well…as we don't know what is going to happen to the other characters.
The twist in the tale is what makes the movie worth it. It's a very satisfying movie although until the last twenty minutes of the movie things seem to be going on in a predictable manner.
Is the movie realistic?
Ofcourse not, but the way it is shot lends it realism. There are no elaborate sets. There are plenty of shots of railway stations, the streets and buildings. A fair amount of the movie takes place indoors, at police HQ.
It was interesting (though I can't say realistic) to see how the director (Neeraj Pandey) portrays Mumbai's senior police officers – very positively. They are shown to get into super action-mode once they get to know of the existence of the bombs…Hollywood style. Hi-tech offices, huge screens, Rathod in charge and barking orders, demanding that everything happen at top speed. They even get a hacker to try and locate the villain!
There is a fair amount of drama in the movie too. There was this conversation between police commissioner Rathod and one of his officers, Jai.
Rathod: Are you married?
Jai: Yes sir.
Rathod: Do you have children?
Jai: A three month old daughter sir
Rathod: Are you ready to die? (Marne ko tayar ho?)
Jai: Yessir!
The characters
Both the main characters are more than just middle-aged…Naseeruddin Shah (who plays the villain) and Anupam Kher who plays Prakash Rathod, the top cop look over 60. There are two young men in the movie – Jai Singh (Aamir Bashir) and Arif Khan (Jimmy Shergill), both police officers. Jimmy Shergill, who plays a ruthless and violent cop is right for the role – he looks physically very fit and does the action scenes convincingly. Anupam Kher does a good job as Chief, although his presence in so many movies is getting to be a bore. Naseeruddin Shah is brilliant as usual…there is something about the way he acts that makes him rise above himself. One never thinks of him as Naseeruddin when one is watching him.
The only woman in the movie is a TV reporter (played by Deepal Shaw) and while she is okay, her role is not in any way critical to the movie.
This movie is worth a see. It's short (100 minutes) and there are no songs, not a single one. The pace of the movie doesn't falter…in fact it keeps building up to an interesting climax. However I was not entirely happy with the editing, although the movie is less than 2 hours in length. There was some unnecessary scenes, mostly played out at police HQ. I think the movie could have been at least 10 minutes shorter although if I compare it to Mumbai Meri Jaan (another movie about terrorism) then I guess the editing of this movie is very good.
(Photo credits: Rediff.com)
Related Reading: Blogger Amit's review
Rock on review
Mumbai Meri Jaan review
Amir review
More: Citizens Need Answers! (on terrorism)
A note to readers: I would be grateful if comments do not reveal the story! Maybe it's a little silly of me to ask for, but would appreciate it! Thanks!
September 14, 2008 12:04 am
I don't think the message of the movie was wrong at all. Though, I do completely agree with the suggestions of Vikram in improving our capabilities.
Our culture, our history, our religion teaches us to be practical in our daily life rather than idealistic maniacs hell bent on living for worthless ideals.
When the terrorists are killing us senselessly, without any care for rule and life of innocents, then it becomes our duty to right the wrong, no matter how. These terrorists are not british and we can not pretend to fight like Gandhi.
These are evil who needs to be destroyed like Kaurvas in Mahabharat. Our heritage places high importance on duty and doing the right thing in right circumstances.
During Mahabharat, Krishna forced Yudhistir to lie to kill Drona, Krishan forced Arjuna to kill Karan when his charriot was stuck in a pothole, and Krishna forced Bhima to defeat Duryodhan by breaking the rules. Even though Krishna broke nearly every rule of the War, he has been worshipped as Bhagawan in India for over 5000 years! You must ask this question yourself, Why is he still considered a Bhagawan? Are people of India stupid to adopt such an Idol?
Same goes for Bhagawan Raam. He killed Bali using "unorthodox" methods. Yet, he is still considered a Bhagawan and has been for over 7000-8000 years! Why?
Krishna and Raam did the most practical and necessary thing to establish the rule of Dharma. Therefore, our culuture, our history, and our society has worshipped them for so many years and adopted them as our idols.
Hindu civilization has placed the utmost importance on doing practical things and following your duty. In the current scenario, the most practical and apt thing to do is to kill these terrorists once we know that they have committed the crime. I hope you don't support keeping Afzal Guru alive just because it may ruffle some imaginary feathers of the followers of "religion of peace".
The true worship of our idols, our bhagwans is to become like them. It is time for each and everyone of us to become Krishna and Raam to protect our Dharma, our civilization and our Nation.
We need to grow up and realize that it is useless to worship at the alters of whishhy washy ideals and we need to live for something tanglible like our Nation.
raghav permalinkSeptember 14, 2008 5:15 am
Great movie. Keeps you busy till the end. A very diff. perspective and the greatest thing is that its abt. a common man's action which makes it more believable.
My condolences to the victims of the next blast in advance wherever its going to be. Srry for my stupid sarcasm. I can't think of more rational way to express my anger.
September 14, 2008 11:47 pm
If killing the terrorists is not the solution then appeasing them is not either.
Why did we have partition? To appease the Muslims and let them live in a separate place so that we can grow in peace. Has it happened? Of Course not.
It is not the time to beg the terrorists to not kill us anymore. We ought to prepare for the war to fight these terrorists. We need to grow a stomach for a tough fight, even it means killing people like Afzal Guru.
People who are living in a wonder world, need to just take a cursory glance at our civilization and history to realize Killing/Violence has been used as effective mean of containing evil. This is the message that is taught to repeatdly through our Puranas, Vedas, Mahabharat, History and so called "mythology".
I doubt any of the preacher of "Killing each other can never be a solution" has been inside a HINDU temple. If you have, you would have noticed that every single Hindu God representation has a WEAPON in their hand. Very often more than 1. Why do you think they are there? For mere decoration?
Hell No! These weapons are suppose to be used to destroy evil. The whole Bhagawad Gita is based on premise that evil appears in various forms, even in the form of our relative/brothers/cousions, and it our utmost responsibility to perform our duty of anihiliating adharma. The results of our actions shouldn't concern us, when we are following our dharmic duty.
The whole western world is grappling with the ways of containing adharmic forces. I hope India can stand up and listen to the message taught and passed on to us for over 5000 years and become a living example of dharmic life.
ulag permalinkSeptember 15, 2008 9:51 pm
It was a good movie. It showed the frustration of a society which is brought to its heels again n again by terrorism. There are some ppl who would like to say no we are not defeated and they would go on to celebrate the "spirit" of the the people, that they are going about their daily lives as usual. In reality this is an illusion. The fact is the terrorists are hitting us and they're hitting us hard where and when they want. They have proved that no target is beyond their reach. To brush this under the carpet is a grave mistake. The fact is that we have systematically been exposed to so much violence over so many years that we have come to accept it. Initially it was confined to Kashmir. Soon it spread to other cities and we told ourselves that it is an outpouring of the situation in Kashmir and once the Kashmir issue is resolved, terrorism will be over. But nowadays not a single terrorist act is linked to Kashmir. We're so used to terrorism that we have not even bothered to wonder why these people are attacking us. They claim to be fighting for minority rights buts its not true. Their real intentions are to destabilize the country.
To top this we have a highly inefficient home minister who makes statements like "I'm sorry that the Delhi blasts have happened"!!!…does our home minister need to apologise for bomb blasts in his own country??
Fact is events like Godhra have given plenty of fuel to feed the fires of revenge. If we ask for stringent laws against terrorism then we must make sure that the same laws and yardsticks are also applied to people who riot and disturb communal harmony. Or else the laws will be seen as biased and unpopular.
Vinod permalinkSeptember 16, 2008 7:00 am
It's short (100 minutes) and there are no songs, not a single one.
I hope the trend picks up. I'm tired of forwarding the song and fight scenes in Indian movies.
Amruta G. permalinkOctober 6, 2008 11:18 am
Yea i find not using due process to prosecute a terrorist quite frightening and akin to terrorism…this movie had serious issues in its portrayal of terrorism and how to take care of it…the "common man" is basically blackmailing the police by threatening to kill hundreds if the one terrorist isn't killed…and this is pretty much what terrorism is and what a terrorist does…india cannot negotiate with terrorists but it cannot kill people without due process…india's judicial system must reform…i'm kinda nervous that all Indians liked this movie so much without being at all critical of it…
aman permalinkFebruary 12, 2012 1:57 pm
nice review….


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SE trim. FUEL EFFICIENT 27 MPG Hwy/21 MPG City! Heated Seats, Moonroof, Satellite Radio, Back-Up Camera, Aluminum Wheels, Turbo Charged, PANORAMIC SUNROOF PACKAGE, All Wheel Drive.
Heated Driver Seat Volkswagen SE with PLATINUM GRAY METALLIC exterior and BLACK LEATHERETTE interior features a 4 Cylinder Engine with 184 HP at 4360 RPM*.
PANORAMIC SUNROOF PACKAGE power tilting and sliding front section and fixed rear section.
"At Moss, You're the Boss!"™
Horsepower calculations based on trim engine configuration. Fuel economy calculations based on original manufacturer data for trim engine configuration. Please confirm the accuracy of the included equipment by calling us prior to purchase.
Pre-Owned 2021 VolkswagenTiguan 2.0T SE SUV
- Exterior Color
- Deep Black Pearl
- Interior Color
- black
- Odometer
- 47,659 miles
- Fuel Economy
- 21/27 MPG City/Hwy
- Transmission
- Automatic
- Drivetrain
- All-wheel Drive
- Engine
- I-4 cyl
- Stock Number
Volkswagen Tiguan
Highlighted Features
- Automatic temperature control
- Wireless phone connectivity
- Exterior parking camera rear
- Front dual zone A/C
- Split folding rear seat
- Heated front seats
- Perimeter/approach lights
- Remote keyless entry
Detailed Specifications
- 1-touch down
- 1-touch up
- Adaptive Cruise Control: Adaptive Cruise Control (ACC)
- Air conditioning
- Automatic temperature control
- Driver door bin
- Driver vanity mirror
- Front beverage holders
- Front dual zone A/C
- Illuminated entry
- Overhead console
- Passenger door bin
- Passenger vanity mirror
- Power windows
- Proximity key: doors and push button start
- Rear beverage holders
- Rear door bins
- Remote keyless entry
- Speed control
- Telescoping steering wheel
- Tilt steering wheel
- Alloy wheels
- Four wheel independent suspension
- Front anti-roll bar
- Front tires: 215/65HR17.0
- Power steering
- Rear anti-roll bar
- Rear tires: 215/65HR17.0
- Speed-sensing steering
- Wheel size: 17"
- 1st row LCD monitors: 2
- AM/FM radio: SiriusXM with 360L
- Diversity antenna
- Primary LCD size: 8.0"
- Radio data system
- Satellite radio trial duration with new vehicle purchase (months): 3
- Smart device integration: Wireless App-Connect (w/Apple CarPlay, Android Auto & MirrorLink)
- Speakers: 6
- Steering wheel mounted audio controls
- Wireless phone connectivity: Bluetooth
- Front center armrest
- Front seats: bucket
- Heated front seats
- Leather shift knob
- Power 2-way driver lumbar support
- Power driver seat
- Rear seat center armrest
- Rear seats: split-bench
- Rear seats Folding position: fold forward seatback
- Seat Upholstery: leatherette V-Tex
- Split folding rear seat
- Compressor: intercooled turbo
- Cylinder configuration: I-4
- Drive type: 4MOTION all-wheel
- Engine liters: 2.0L
- Engine location: front
- Fuel economy city: 21mpg
- Fuel economy combined: 24mpg
- Fuel economy fuel type: gasoline
- Fuel economy highway: 27mpg
- Fuel tank capacity: 15.9gal.
- Horsepower: 184hp @ 4,360RPM
- Hybrid traction battery type: none
- Manual-shift auto: Tiptronic
- Mode select transmission
- Number of valves: 16
- Recommended fuel: Regular Unleaded
- Torque: 221 lb.-ft. @ 1,600RPM
- Transmission: 8 speed automatic
- Variable valve control
- Approach angle: 26 deg
- Departure angle: 23 deg
- Ground clearance (min): 201mm (7.9")
- Ramp breakover angle: 19 deg
- Bumpers: body-color
- Door mirrors: body-color
- Heated door mirrors
- Power door mirrors
- Rear cargo: liftgate
- Spoiler
- Trailer sway control
- Turn signal indicator mirrors
- Compression ratio: 11.65 to 1
- Engine bore x stroke: 82.5mm x 92.8mm (3.25" x 3.65")
- Engine displacement: 2.0 L
- Engine horsepower: 184hp @ 4,360RPM
- Engine torque: 221 lb.-ft. @ 1,600RPM
- Exterior body width: 1,839mm (72.4")
- Exterior height: 1,684mm (66.3")
- Exterior length: 4,702mm (185.1")
- Front headroom: 1,006mm (39.6")
- Front legroom: 1,021mm (40.2")
- Front shoulder room: 1,448mm (57.0")
- Towing capacity: 680kg (1,500lbs)
- Turning radius: 5.7m (18.8')
- Wheelbase: 2,789mm (109.8")
- Appearance: analog
- Blind spot: Side Assist warning
- Compass
- Delay-off headlights
- Exterior parking camera rear
- Front reading lights
- Fully automatic headlights
- Low tire pressure warning
- Outside temperature display
- Rear reading lights
- Rear window defroster
- Rear window wiper
- Tachometer
- Trip computer
- Variably intermittent wipers
- 4 wheel disc brakes
- ABS brakes
- Brake assist
- Dual front impact airbags
- Dual front side impact airbags
- Electronic stability
- Forward collision: FCW w/Autonomous Emergency Braking mitigation
- Ignition disable
- Occupant sensing airbag
- Overhead airbag
- Panic alarm
- Pedestrian detection: prevention
- Perimeter/approach lights
- Rear collision: Rear Cross Traffic Alert mitigation
- Security system
- Traction control
Dealer Notes
KBB.com Consumer Reviews
- 5.0
3 years later, I finally bought one
By Oakie on Wednesday, May 01, 2019I have researched the Tiguan for three years. In 2018, I fell in love with new design. Bought a 2019 SEL Premium 4 Motion R-Line. I wanted to wait till I got some miles on it and months of ownsership before I wrote a review. I have to tell you that I have seen several comments about poor performance. I haven't experienced it after break in and getting used to stiffer German engineered gas pedal. I was used to it after having a MB C300. Anyway, without using sport mode, I can take off and leave traffic behind at a stop light. Sport mode is even quicker. The ride is nothing short of luxurious, quiet and solid. The stereo (Fender) is as good as my Burmeister was in the MB. Great bass. The seats are magnificent, contour and comfort are great. My 91 year old father loves them too. The digital dash and center display are fantastic, intuitive and very useful. The fit and finish of the car is amazing. As is usual with German cars, everything is over engineered and sturdy. The panoramic sunroof is big, well visible from front seat and dazzling in back seats. The electric sunshade never fails to impress riders. The adaptive LED headlights are bright and impressively capable. The LED corner lights that light up at turn of wheel after slowing are hella bright. I love them and they are truly useful. Overall, the car is super luxurious, fun and steers better than any car I have ever had. Don't take my word for it as a happy buyer. Take it for a test ride yourself. You'll be amazed. I must say the fantastic warranty was a plus and for about $1,200, I purchased the additional warranty for 96 months or 120k miles. Best of all, it takes 87 octane regular unleaded ONLY. Says so right on the gas cap. Anyone that has a Tiguan knows what I am saying here is factual. I love mine.
- 5.0
2019 Tiguan SEL 4 MOTION
By Mike on Thursday, September 19, 2019I just bought a 2019 VW Tiguan SEL 4MOTION . Black exterior Black Interior. The inside is very sleek techy comfortable and the cabin is quiet when driving. The only gripe I have with this car is the very small low center console and the power of the engine , although it does have a Turbo starting from a green light the power is very minimal. Handles very well and has a quiet smooth ride. Ive never owned a VW before and this is my first and so far I absolutely love it and everyone that has seen it and the few I let drive it , love it.
- 5.0
Great vehicle
By Creek on Monday, September 09, 2019This was our first new car in 7 years. We purchased the highest available trim with all the bells and whistles. Pros: Looks great. Higher than advertised fuel economy (driving the speed limit on highway yields about 31 mpg). I love the auto stop feature while sitting at traffic lights. Android Link is great! The car remembers my settings and will automatically adjust my seats according to my key. I love the digital dashboard. Auto high beams and windshield wipers. Lane assist and adaptive cruise control. Cons: The seats are a little firm.


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Sales & Service: 337-264-1441 9:00 AM - 5:00 PM CST| Mon - Fri
Item # 9031326
Delivery time: 5-10 Business Days
When you see the "GM Restoration Parts" emblem associated with our items, you can rest assured that part is license by General Motors for reproduction and meets the GM guidelines for quality and authenticity. TrimParts products are fully guaranteed against any manufacturing defects. We believe you deserve high quality authentic products and TrimParts manufactures all of their items with your total satisfaction in mind.
Best fit and arrived sooner than stated will be ordering more parts from them soon-Nick G., White lake, MI


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Massive power outages as Northeast blizzard turns deadly
- The storm is being blamed on at least four deaths in New York and Canada
- Hundreds of cars stuck on the Long Island Expressway
- The Pilgrim Nuclear Power Plant in Plymouth experienced an automatic shutdown
A blizzard predicted to be of epic proportions is pounding the Northeast, already bringing more than a foot of snow to some areas as 40 million residents in its path brace for the worst.
As of 5:20 a.m. ET, more than 650,000 homes and businesses had lost electricity as wet snow, freezing rain and howling winds caused havoc.
More than 28 inches of snow has fallen in central Connecticut, and areas of southeastern Massachusetts, Rhode Island and New Hampshire stand at 2 feet or more.
And the worst is not expected until later Saturday, the National Weather Service warned. Blizzard warnings are in effect for the New York City metro area and many coastal sections of New England. Hurricane winds of up to 75 mph are also possible.
As part of a new effort to name winter storms, the Weather Channel dubbed the blizzard "Nemo."
Finding Nemo hasn't been an issue: it's been leaving noticeable havoc. Police in New York say hundreds of cars have gotten stuck on the Long Island Expressway due to the blizzard conditions and dozens of disabled motorists are still on the road. The Long Island Expressway and Sunrise Highway are both shut down in Suffolk County except for emergency vehicles. The snow also caused a 19-car, four-hour pileup on I-295 near Cumberland, Maine. Several people had minor injuries, police said. In Vermont, which could get 4 to 16 inches of snow, the storm was being blamed for a series of crashes on I-89 in Bolton and South Burlington. Two people were taken to the hospital with minor injuries.
The storm is being blamed on at least four deaths in New York and Canada.
More than 5,200 flights in the region had been canceled through Saturday, according to flight-tracking service FlightAware. New York City's three major airports and Boston's Logan Airport are closed. Flights were also canceled at Toronto's Pearson International Airport, where nearly a foot of snow was forecast. Amtrak suspended southbound service out of Boston and northbound service out of New York City on Friday afternoon.
By 6 p.m. Friday, Wayne N.J., had 7 inches, Darien, Conn., 6 inches and parts of the New York metro area had received 2.5 inches. Connecticut, Rhode Island and Massachusetts had already declared a state of emergency. New York Gov. Andrew Cuomo declared a state of emergency Friday afternoon as the storm intensified.
Maine Gov. Paul LePage sent state workers home at 3 p.m. and declared a limited emergency to allow longer hours for utility crews. Massachusetts Gov. Deval Patrick banned all traffic from roads Friday afternoon, believed to be the state's first such ban since the blizzard of 1978. Forecasters said Boston could get more than the 27.6-inch record of 2003.
Utility officials are warning customers to prepare for power outages lasting for days. New England and New York are expected to take the hardest hit, but others around the country could feel the ripple effect from canceled flights trains and snarled traffic along the Eastern Seaboard, parts which are still reeling from the fallout of October's Superstorm Sandy.
Northeast New Jersey was bracing for up to 14 inches. Parts of the coast were expected to see waves up to 12 feet and minor to moderate flooding during high tide.
In New Jersey, residents of Brick Township and Toms River, both crippled by Sandy, were urged to evacuate Friday.
Newark Mayor Cory Booker urged residents to prepare for widespread power failures. Booker, a prolific Twitter user, urged his nearly 1.4 million followers to get ready for the storm. "Nwk's City Snow Team is prepared for 6-12 inches," he tweeted from @corybooker a couple minutes after 5 p.m. on Thursday. "We have many snow assets in reserve should storm get worse. Please take time 2 prepare too."
STORY: Airline cancellations soar
YOUR WEATHER: Send us your snow photos
New York City Mayor Michael Bloomberg said the blizzard wasn't expected to rival Sandy's fallout, but urged everyone to "stay in your homes while the worst of the storm is upon us."
He urged New Yorkers to leave work early and avoid commuting Friday evening, when meteorologists predict the snowfall to intensify.
Bloomberg said there were no immediate plans to declare a storm emergency, because that would require vehicle owners to move them off emergency routes – raising the potential some could get stuck and block snowplows.
Similarly, Bloomberg did not order evacuations from low-lying areas, explaining that storm surges were not expected to reach Sandy's disastrous levels. Still, the city will have emergency shelters open and available for anyone who needs assistance, he said.
About 1,700 city Department of Sanitation snowplows were ready to start clearing streets Friday evening.
The New York City metro area, home to three airports and 20 million residents in four states, was bracing for up to 12 inches of snow, according to AccuWeather meteorologist Alex Sosnowski.
At 7 p.m. in downtown Boston, wind picked up to a point to where pedestrians had to occasionally hold onto light poles to keep from being blown down the street. Snow fell sideways and stung faces like needles.
Outside John B. Hynes Veterans Memorial Convention Center, David Comar and workers shoveled as vigorously as the snow fell.
The team had been out since 1 p.m. and would work until about 9, when conditions were expected to intensify, said supervisor Jimmy Figueroa.
A couple of blocks away, Oscar Medrano, an employee of Central Parking Systems, continually drove a truck with plow through a small parking lot. Like the men outside the convention center, he'd also started in the afternoon. Medrano said he would keep shoveling until midnight.
"Just keeps coming," said Medrano, 40.
Massachusetts is keeping residents informed through a 2-year-old hyperlocal app called Ping4, which sends localized alerts to mobile phones.
Ping4 has the ability to send alerts only to phones within an affected geographical area so that people are not pummeled with alerts that do not affect them, said Jim Bender, founder and CEO of Ping4, based in Nashua, N.H.
In Boston, Mayor Thomas Menino said the city has 34,000 pounds of salt to treat icy roads. "Stay off the roads. Stay home. Let the public works crews do their jobs," Merino said.
The Pilgrim Nuclear Power Plant in Plymouth experienced an automatic shutdown at around 9:15 p.m. Friday after losing off-site power. Spokesman Neil Sheehan says that the reactor shut down without any problems and that backup generators are powering plant equipment.
The Nuclear Regulatory Commission says there's no threat to public safety.
As several businesses closed early to prepare for the storm, Downtown Wine & Spirits in Somerville, Mass., prepared for one of its busiest days this year. "The second most important thing besides food is booze," said Downtown Wine & Spirits wine buyer Peter Powlovich, 29.
With extra staff and beer, the liquor store remains open for normal business hours unless there's a power outage, Powlovich said.
The storm isn't expected to have a major economic impact on New England, said economist David Iaia of Lexington, Mass.-based IHS Global Insight.
"If everything just shuts down for a day, the vast majority of business merely gets shifted to before the storm or after the storm," Iaia said.
Anticipating the storm's impact, every big U.S. airline has issued flexible re-booking policies. The move allowed most fliers ticketed to fly to airports in the storm's path to make one change to their flights without the standard change fees.
With such a large number of cancellations, the flight disruptions in New York and the Northeast are all but certain to ripple through airports across the nation. A flight from Houston to Los Angeles, for example, could become delayed or canceled if the aircraft or crew scheduled to fly it gets knocked off schedule because of problems in Boston or New York.
Snarled transportation aside, ski resorts all over New England are excited about the biggest snowfall of the season.
"If I had a tail, it would be wagging," says Stowe Mountain Resort spokesman Mike Colbourn. "Presidents (Day) week is next week, a big nor'easter – all of the stars are in alignment."
"As far as where the big ski areas are, we are at ground zero for this storm — we are in the 24-inch band," says Bruce McCloy, director of Marketing for Mount Sunapee Resort in Newbury, N.H., "We are so excited! It's going to be awesome. How are we getting ready? We are dancing a jig, and then after that, we are getting ready. We haven't had any big storms in the past two years, so this is really big."
Contributing: Melanie Eversley, Ben Mutzabaugh, Stephanie Haven; Alesha Williams, Laura Petrecca, Natalie DiBlasio, TIm Mullaney; Associated Press


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Swimmer Rose Gold Sandal
Info & Care
The Swimmer features a plaited leather toe with buckled ankle strap. Fits narrower than the Salt-Water Original, and as the front is non-adjustable, not the best for very narrow or wide feet.
Delivery & Returns
Across Asia we offer a range of services including Standard Delivery, Express Delivery and Free Shipping, Free Delivery over $100.00*
*only available in applicable countries.
For special delivery inc Express, we offer a door-to-door service (not regular mail) and there must be someone at the address in normal working hours to receive the delivery. Sometimes a work address is a better option for this reason. We will deliver the package to the address but not person-to-person, so please guarantee a trusted person will be there to receive the package.
We ask that all special delivery is ordered pre 11am for same day despatch.
We will deliver the package to the address but not person-to-person, so please guarantee a trusted person will be there to receive the package.
For regular mail, postage can take between 2-5 days and final costs will be worked out at checkouts dependant on postcode/address/weight/dims.
Final delivery costs will be calculated at checkout using your address, postcode, item weight and dimensions.
Holiday Deliveries
Please note during national holiday periods (Easter / Christmas / Bank Holidays) delivery and despatch will be slower. Our warehouse and all Courier services also deserve a break with their families and often we rely on a skeleton staff of eager beavers.
Sun-San & Salt-Water Sandals that are purchased online from our webstore can be returned within 28 days of the purchase date for a full refund of the amount of the purchase. Upon receiving your returned Sandals at our warehouse, a refund for the amount of the purchase will be issued to you within 14 business days. This refund will be issued to the same payment method that was used to make the original purchase. We cannot refund different accounts or credit cards. All merchandise must be returned unused and accompanied by the original box and packaging.
South-East Asia & Middle East Customer Returns
If you're looking to return a pair of sandals purchased from our webstore, please fill out the form you received with your order including the order number reference and send it via a recorded delivery service back to us at:
Salt-Water Sandals Asia PTE Ltd
c/o Whitebox PTE Ltd
222 Tagore Lane
#02-18 TG Building
Singapore 787603
Please note that all returns must be returned in the original shoe box with external packaging. If your return is received with a damaged shoe box, you will have a USD$5.00 deduction from your refund to cover the costs of repackaging.
We cannot accept responsibility/reimburse for any lost or damaged items so please do use a trackable service and keep your proof of postage.
Additional Information
All merchandise must be returned unused and accompanied by the original shoe box and packaging. If your return is received with a damaged shoe box you will have a USD$5.00 deduction on your refund to cover the costs of repackaging.
Please make sure you try on your shoes on a carpeted area. We will not accept returned shoes that are marked on the sole. The condition of the product is left to the discretion of Salt-Water.
All returned items must include information on the order (full name/email address/order number/items returned) for your refund to be processed.
Do not use the shoe box as outer packaging as it is counted as part of the sold unit.
Our Adult Swimmer takes the Original woven upper and reinvents it with a soft sole sandal base.


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Style J US
Midnight Mermaid Long Denim Skirt # TA-0631
$ 55.00
Style J – Size Tips
Size Tips: Our sizes are labeled to reflect waist size. You will find detailed measurements
of each skirt on the style's page.
Please check carefully for your individual size measurements before ordering.
If you are not sure about your waist size, you can measure the waistband of a skirt you own.
Lay the skirt flat on the table, measure from the left to the right
without stretching out the skirt, then double your measurement.
For example, if your measure result is 17",
then you double it (17" x 2 = 34"), that means the skirt waistband measurement is 34".
Use this measurement to refer to the size chart to find what size skirt you should order.
Make sure to take your hip size into consideration.
You can measure the fullest part of your hips to match the size chart
to ensure your skirt will be a good fit.
How to read our size chart:
Size: Label on the skirt.
US Size: Recommended size comparison based on the standard US clothing size for skirts.
Skirt Waistband: The measurement of the skirt's waistband. To measure a skirt's waistband,
lay it on a flat surface and measure from left to right, then double that number for
the skirt waistband size.
Skirt Hips: Generally, the skirt's hip size is measured between 6"~8" below the waistband.
This can vary with different styles. To measure a skirt's hip size, lay it flat on a surface and
measure 6"~8" below (for low-rise cut skirt, usually measure 6"~7" below) the waistband.
At that spot, measure left to right and double the number to get the skirt's hip size.
Bottom Width: The bottom width of the skirt. Note: This measurement is NOT the circumference
of the skirt.
Skirt Length: Measurement from the top of the skirt (the waistband) to the bottom of the skirt.
Style J – Return Policy
Returns are at your discretion, but items must be returned in new condition with company tags and packing slip. If you no longer have the packing slip, please include a note indicating: your name, address, the items you are returning and any other pertinent information.
All the "Final Sale" items are final. No exchanges or returns are accepted. Customers are responsible for return postage. Shipping charge is not refundable except on orders that we shipped incorrectly.
If a domestic customer elects to exchange an item(s) for a different size or style, you must return the item to us at your own cost and Style J will pay the postage to ship the replacement (This free exchange shipping is limited to one time exchange only). International customers will be charged the shipping cost for the exchange.
All returns must take place within 15 days of receipt of items (We extend the return period to 30 days during the months of December and January).
Please note that our discount coupon does not apply to your exchange items.
International orders can only be processed with PayPal payment method.
Please make your check payable to "Style J LLC" if you would like to pay with a money order. We will hold your item(s) for 10 days. Thank you.


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My explorations into the formulas in Peter Reinhart's The Bread Baker's Apprentice continue with this festive little number, the Christoposomos, one of the Greek Celebration bread variations.
This was both exhilarating and challenging for me…nope, I never thought I'd qualify the craft of bread baking as exhilarating, but I'm learning to better appreciate all that I'd taken for granted as being easy or boring or plain in my youth, and yes, this is wild and crazy stuff! No dowdy submissive chica in the kitchen here, kids, just one punk rock veganfish listening to The Dead Milkmen and stripping the animal products from this delicious recipe.
All the recipes I've made so far from Apprentice have been very easily veganizable, and this was no exception. I used agave syrup to sub out the honey and Ener-G for the two large eggs.
I used coconut milk in this recipe because I wanted to be sure to add enough fat to the dough, and the results were just perfect. There was no lasting coconut flavour in the finished bread, but the coconut milk did lend a lovely buttery quality that was just perfect.
While this isn't a recipe I will make often, I will indeed save this one for special occasions or for when we have guests for breakfast or brunch. It's rather fancy and far more sophisticated than anything I've ever made bread-wise before, and I felt like a rock star yet again! Perhaps I'm just too easily amused?
I'd like to dedicate this Celebration Bread to Susan of Wild Yeast as she is celebrating the First Anniversary of Yeast Spotting this week! I think that is indeed reason to celebrate!


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NEW YORK (AP) - The hang time is over for Ray Guy. The longtime punter for the Oakland Raiders is all by himself once again.
After waiting 23 years, Guy is the first punter elected to the Pro Football Hall of Fame.
"Good things are worth waiting for," Guy said Saturday night after being elected along with six other players. "It's just a matter of time when it will show up. And I knew it would, sooner or later. It had to, whether it was me or somebody down the road. But sooner or later, it had to show up, because that is a part of a football game."
Defensive end Michael Strahan, receiver Andre Reed, defensive back Aeneas Williams and defensive end Claude Humphrey also were part of the class of 2014. Two first-time eligible players, linebacker Derrick Brooks and offensive tackle Walter Jones, were selected.
The announcement was made at the NFL Honors award show, less than 24 hours before the Denver Broncos take on the Seattle Seahawks in the first Super Bowl.
Among the finalists who didn't get in were two with ties to the Indianapolis Colts and current Broncos quarterback Peyton Manning - coach Tony Dungy and receiver Marvin Harrison.
Each incoming Hall of Famer walked to the stage and was announced individually. Strahan, who helped the Giants make two Super Bowls, got a huge cheer from the home crowd.
Induction will be on Aug. 1 in Canton, Ohio.
Guy turned the punting job into a defensive weapon after he became the first player at his position to be selected in the first round of the draft in 1973. He made "hang time" part of the football vernacular while playing all of his 207 games in 14 seasons with the Raiders.
The Southern Mississippi product averaged 42.4 yards for his career. Only three of his 1,049 punts were blocked, and he had 209 punts downed inside the 20-yard line.
"It's gratifying to now see a punter go into the Hall of Fame," Guy said, who joins Jan Stenerud as the only kickers enshrined . "Whether it was me or somebody else, they needed representation in that position."
Brooks was the cornerstone of a Bucs defense that led the league in 2002 and '05, and the NFC five times. He was The Associated Press Defensive Player of the Year when Tampa Bay won its only Super Bowl after the 2002 season.
The linebacker never missed a game in his 14 seasons and averaged a remarkable 146 tackles. Six of his 25 interceptions were returned for touchdowns, including a league-record three in '02.
Seattle certainly got a winner when it moved up to the No. 6 spot in the 1997 draft to take Jones. He immediately provided blindside protection for Warren Moon and quickly became the first Seahawks lineman to earn a Pro Bowl spot. He was one of the chief road graders who helped Shaun Alexander rush for 266 yards in a 2001 game - the fourth-highest total in NFL history - and then rush for a team-record 1,880 yards and 28 TDs in his MVP season in 2005.
"Coming into the league all I wanted to do was get here, and … say I could play this game," Jones said. "For me to be here now, and for my team that I started with and finished with, to be here in the Super Bowl is just like the icing on the cake."
Strahan set the NFL record for sacks in a single season, getting 22½ in 2001. The one most people remember is the record-setter in the final game of the regular season, when Green Bay's Brett Favre seemed to lay down on a play late in the game.
While there is controversy about that play, the gap-toothed Strahan was one of the top two-way defensive ends. Younger teammates said he taught them how to work to become NFL players, and he walked away from the NFL after winning the Super Bowl in February 2008.
"It's hard to find guys with everything, but this guy had everything . size, speed, power, toughness, endurance, motor, smarts, leadership, heart, love for the game, but what I admired most about Michael was his pride," Giants general Jerry Reese said. "No matter what the circumstances were, when he walked out on that field on Sunday, he was going to give it ALL to you. There aren't many guys who can say that."
Reed came out of little Kutztown (Pa.) University and played his first 15 seasons with Buffalo, getting to four Super Bowls, but never winning one. His final season was with Washington. His 951 career receptions are third in league history, highlighted by nine consecutive seasons of 50-plus catches.
Long before people spoke about yards after the catch, Reed was doing it. He finished with 13,198 yards and 87 touchdowns.
"Having to wait this long for him is a sin, but the bottom line is he's in and that's what counts," former Bills quarterback Jim Kelly said of Reed's nine-year wait to get into the Hall.
A walk-on at Southern University, Williams was a shutdown cornerback in his 14 NFL seasons, the first 10 with the Cardinals and the last four with the Rams. He had 55 career interceptions, getting at least one in every season except his last. He had five or more in picks in six seasons, with nine being his best in 1994.
Williams spent his last four seasons with St. Louis. He started at cornerback for the Rams in the 2001 Super Bowl and played safety in his final two seasons.
The Hall of Fame doors finally opened for Humphrey on his 28th year of eligibility and his fifth as a finalist. The durable six-time Pro Bowl pick had 122 career sacks in 14 seasons with the Falcons and Eagles, who acquired him after a brief retirement in the 1978 season.
"I never really gave up hope," said Humphrey, whose only regret was his wife died in July and didn't get to see his election. "I always figured there was a place for me here."
AP NFL website: www.pro32.ap.org
AP Sports Writers Tim Booth and Dennis Waszak Jr., and Pro Football Writer Howard Fendrich contributed to this story.
Copyright © 2023 The Washington Times, LLC.
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Almost everyone has, or will, play a crossword puzzle at some point in their life, and the popularity is only increasing as time goes on. Crosswords themselves date back to the very first crossword being published December 21, 1913, which was featured in the New York World. The crossword was created to add games to the paper, within the 'fun' section.
However, crosswords are as much fun as they are difficult, given they span across such a broad spectrum of general knowledge, which means figuring out the answer to some clues can be extremely complicated. It's not shameful to need a little help sometimes, and that's where we come in to give you a helping hand, especially today with the potential answer to the *William S. Burroughs novel crossword clue.
*William S. Burroughs novel Crossword Clue Answer
Below is the potential answer to this crossword clue, which we found on September 27 2022 within the LA Times Crossword. It's worth cross-checking your answer length and whether this looks right if it's a different crossword though, as some clues can have multiple answers depending on the author of the crossword puzzle.
- 10 Letters
We've also got you covered in case you need any further help with any other answers for the LA Times Crossword Answers for September 27 2022.
Hopefully that solved the clue you were looking for today, but make sure to visit all of our other crossword clues and answers for all the other crosswords we cover, including the NYT Crossword, Daily Themed Crossword and more.
Check back tomorrow for more clues and answers to all of your favourite crosswords and puzzles.


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Today's News: Our Take - How I Met Your Mother Casts a Pretty Little Liar! Plus: Who Is Coming Back?
Pretty Little Liars star Ashley Benson is taking a break from the tireless search for "A" to romance someone from How I Met Your Mother, TVLine reports.
Benson, 22, will play an unconventional love interest for one member of the gang in the Jan. 21 episode. Could it be Barney (Neil Patrick Harris)? Or Ted (Josh Radnor)? Or maybe even Robin (Cobie Smulders)? Hey! It could happen.
Ian Somerhalder? Sofia Vergara? Make your picks for TV's sexiest eye candy now!
In other casting news, the show's make-up department head Jennifer Turchi tweeted news that two familiar faces would be returning: Ray Wise as Robin's dad and Rachel Bilson as Ted's former student. CBS would not confirm their returns, but co-creator Carter Bays did tell TVGuide.com that someone from Ted's past will have a "big influence on his search for the mother." Hmmmm...
How I Met Your Mother airs Mondays at 8/7c on CBS. Who do you think Benson will romance on the show? Are you excited for Wise and Bilson's returns? Sound off below!
View original How I Met Your Mother Casts a Pretty Little Liar! Plus: Who Is Coming Back? at TVGuide.com
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