- #1

Agent Smith

- 61

- 3

*Vide supra*is a first few stages of Pascal's Triangle. The numbers themselves are the coefficients for the binomial expansion of ##(a + b)^n##, where ##n \in \{0, 1, 2, ... \}##. I'm just curious whether each stage has a special meaning, unique to it. My lack of knowledge prevents me from giving examples; my best shot is that ##(a + b)^0 = 1##, we know ##1## is special, it's the foundation of counting and hence arithmetic. I hope that suffices to get my point across.

I've highlighted the 6th stage of Pascal's triangle with a red rectangle and consists of the coefficients of the terms of ##(a + b)^6 = 1a^6b^0 + 6a^5b + 15a^4b^2 + 20a^3b^3 + 15a^2b^4 + 6a^1b^5 + 1a^0b^6## because I'd like to know if ##(a + b)^6## is special in any way e.g. (pure speculation) the coefficients give us the number of dimensions in which the Pythagorean theorem is false.

Gracias.