The saga of great theorems. Pascal’s triangle and Newton’s binomial. (La saga des grands théorèmes.) (French) Zbl 1519.11008
The “great theorem” in this volume is Pascal’s triangle and Newton’s binomial theorem. Pascal’s triangle was already studied by al-Karaji and Yang Hui, and Pascal applied it to combinatorial problems in probability. Newton’s binomial theorem, the development of \((a+b)^m\) for rational numbers \(m\), allowed him to determine power series for functions such as \(\arcsin x\).
Reviewer: Franz Lemmermeyer (Jagstzell)
MSC:
11B65 | Binomial coefficients; factorials; \(q\)-identities |
05A10 | Factorials, binomial coefficients, combinatorial functions |