檔案:PascalTriangleAnimated2.gif

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PascalTriangleAnimated2.gif(260 × 240 像素,檔案大小:28 KB,MIME類型:image/gif、循環、84幀、12秒)

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Pascal's triangle is a geometric arrangement of integers representing the binomial coefficients in a polynominal equation of the format (x + y)n. The formation also demonstrates many other mathematical properties, such as listing the entire set of the natural numbers in the first diagonal rows. This phenomenon is named after Blaise Pascal in the western world, however was studied in detail before his time in many Asian countries.

It is also called the Halayudha's triangle, in honor of the Sanskrit prosody scholar who described it. (See: Alexander Zawaira and Gavin Hitchcock (2008), A Primer for Mathematics Competitions, Oxford University Press, ISBN 978-0-19-156170-2, page 237)

It is alternately referred to as "Khayyam's triangle" after the Persian Omar Khayyám. 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.

This version has the 1 cells already filled in, and includes actual animation to better demonstrate the construction.
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來源 自己的作品
作者 Hersfold on the English Wikipedia
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PascalTriangleAnimated.gif

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目前2012年5月3日 (四) 03:45於2012年5月3日 (四) 03:45的縮圖版本260 × 240(28 KB)Dratini0Optimized and fixed with Gimp, because it did not work for me in LibreOffice and Gimp. I might have made a mistake.

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