PascalTriangleAnimated2.gif
Summary
Description PascalTriangleAnimated2.gif |
English:
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.
Čeština:
Animace zobrazuje vytváření
Pascalova trojúhelníku
.
|
Date | |
Source | Own work |
Author | Hersfold on the English Wikipedia |
Other versions |
Licensing
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I, the copyright holder of this work, release this work into the
public domain
. This applies worldwide.
In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose , without any conditions, unless such conditions are required by law. |