File:PascalTriangleAnimated2.gif
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PascalTriangleAnimated2.gif (260 × 240 pixels, file size: 28 KB, MIME type: image/gif, looped, 84 frames, 12 s)
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
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| current | 12:15, 5 January 2017 | | 260 × 240 (28 KB) | 127.0.0.1 (talk) | <p><a href="https://en.wikipedia.org/wiki/Pascal%27s_triangle" class="extiw" title="w:Pascal's triangle">Pascal's triangle</a> is a geometric arrangement of <a href="https://en.wikipedia.org/wiki/integers" class="extiw" title="w:integers">integers</a> representing the <a href="https://en.wikipedia.org/wiki/binomial_coefficients" class="extiw" title="w:binomial coefficients">binomial coefficients</a> in a polynominal equation of the format (x + y)<sup>n</sup>. The formation also demonstrates many other mathematical properties, such as listing the entire set of the <a href="https://en.wikipedia.org/wiki/natural_numbers" class="extiw" title="w:natural numbers">natural numbers</a> in the first diagonal rows. This phenomenon is named after <a href="https://en.wikipedia.org/wiki/Blaise_Pascal" class="extiw" title="w:Blaise Pascal">Blaise Pascal</a> in the western world, however was studied in detail before his time in many Asian countries. </p> <p>It is also called the Halayudha's triangle, in honor of the <a href="https://en.wikipedia.org/wiki/Sanskrit_prosody" class="extiw" title="w:Sanskrit prosody">Sanskrit prosody</a> scholar who described it. (See: Alexander Zawaira and Gavin Hitchcock (2008), A Primer for Mathematics Competitions, Oxford University Press, <a href="//commons.wikimedia.org/wiki/Special:BookSources/9780191561702" class="internal mw-magiclink-isbn">ISBN 978-0-19-156170-2</a>, page 237) </p> <p>It is alternately referred to as "Khayyam's triangle" after the <a href="https://en.wikipedia.org/wiki/Persia" class="extiw" title="w:Persia">Persian</a> <a href="https://en.wikipedia.org/wiki/Omar_Khayy%C3%A1m" class="extiw" title="w:Omar Khayyám">Omar Khayyám</a>. Each number is the sum of the two directly above it. This animation shows this relation in the construction of the first five rows, however the pattern applies for an infinite range. </p> <p>This version has the 1 cells already filled in, and includes actual animation to better demonstrate the construction. </p> |
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