Star of David theorem
Encyclopedia
The Star of David theorem is a mathematical result on arithmetic
properties of binomial coefficients. It was discovered by H.W. Gould in 1972.
s of binomial coefficients forming the Star of David
shape in Pascal's triangle
, are equal:
Arithmetic
Arithmetic or arithmetics is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations. It involves the study of quantity, especially as the result of combining numbers...
properties of binomial coefficients. It was discovered by H.W. Gould in 1972.
Statement
The greatest common divisorGreatest common divisor
In mathematics, the greatest common divisor , also known as the greatest common factor , or highest common factor , of two or more non-zero integers, is the largest positive integer that divides the numbers without a remainder.For example, the GCD of 8 and 12 is 4.This notion can be extended to...
s of binomial coefficients forming the Star of David
Star of David
The Star of David, known in Hebrew as the Shield of David or Magen David is a generally recognized symbol of Jewish identity and Judaism.Its shape is that of a hexagram, the compound of two equilateral triangles...
shape in Pascal's triangle
Pascal's triangle
In mathematics, Pascal's triangle is a triangular array of the binomial coefficients in a triangle. It is named after the French mathematician, Blaise Pascal...
, are equal:
External links
- Star of David theorem, from MathWorldMathWorldMathWorld is an online mathematics reference work, created and largely written by Eric W. Weisstein. It is sponsored by and licensed to Wolfram Research, Inc. and was partially funded by the National Science Foundation's National Science Digital Library grant to the University of Illinois at...
. - Demonstration of the Star of David theorem, in MathematicaMathematicaMathematica is a computational software program used in scientific, engineering, and mathematical fields and other areas of technical computing...
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