PascalTriangleAnimated2
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.
Relevantní obrázky
Relevantní články
Pascalův trojúhelníkPascalův trojúhelník je geometrické uspořádání binomických koeficientů do tvaru trojúhelníku. Jednotlivé položky trojúhelníku se vyplní podle pravidla, kdy každá položka je součtem dvou položek nad ní. Tuto skutečnost představuje rovnice: .. pokračovat ve čtení