Relations between e, $π$, golden ratios and $\sqrt{2}$

We write out relations between the base of natural logarithms ($e$), the ratio of the circumference of a circle to its diameter ($π$), the golden ratios ($Φ_p$) of the additive $p$-sequences, and the ratio of the diagonal of a square to its side ($\sqrt{2}$). An additive $p$-sequence is a natural extension of the Fibonacci sequence in which every term is the sum of $p$-previous terms given $p \ge 1$ initial values called seeds.

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