A journey to Binomia
DOI:
https://doi.org/10.55630/mem.2023.52.180-191Keywords:
Binomial coefficients, Pascal triangle, Newton’s binomialAbstract
In his book “Mathematical discovery” George P´olya starts from the question in how many different ways one can read the magic word “abracadabra”, written in a square with repetitions of the letters, translates the problem in the language of paths in the streets of New York, and in this way he introduces the binomial coefficients and the Pascal triangle. The purpose of our paper is to make a few more steps and during a journey in the fictional country Binomia to present also other properties of the binomial coefficients and the Pascal triangle.
References
B. Pascal. Trait´e du triangle arithmetique: avec quelques autres petits traitez sur la mesme mati`ere. 1654, published 1665, https://cudl.lib.cam.ac.uk/view/PR-CCB-00013-00024/1 (8.03.2023).
G. Polya. ´ Mathematical discovery: On understanding, learning, and teaching problem solving. New York-London-Sydney, John Wiley and Sons, Inc. Vol. I, 1962, Vol. II, 1965.
Pascal’s triangle, https://en.wikipedia.org/wiki/Pascal%27s_triangle (8.03.2023).
D. Poya. Matematicheskoto otkritie: Za razbiraneto, izuchavaneto i obuchavaneto v reshavane na zadachi. Sofiya, Narodna prosveta, 1968.
