Higher dimensional visual proofs, Nicomachus' 4D Theorem and the mysterious irreducible factor $(3n^2+3n-1)$ in the sum of fourth powers

Urtzi Buijs

Sums of powers $S_p(n)={\sum }_{k=1}^n{k}^p$ can be described by Faulhaber's formula in terms of the Bernoulli numbers. The first cases of this formula admit visual proofs of various k…