A Rigorous Geometric Proof of the Formula $\sum \limits_{k=1}^{n}(2k-1)=n^2$ and Its Connection to the Binary Goldbach Problem

Theophilus Agama

A Rigorous Geometric Proof of the Formula $\sum \limits_{k=1}^{n}(2k-1)=n^2$ and Its Connection to the Binary Goldbach Problem

In this paper we give a geometric proof of the fact that the sum of all odd numbers up to any given threshold is always a perfect square. We then relate this fact to the binary Goldbach conjecture, one of the oldest unsolved problem in mathematics.

Comments: 4 Pages.

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[v1] 2020-10-19 19:39:51

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General Mathematics

A Rigorous Geometric Proof of the Formula $\sum \limits_{k=1}^{n}(2k-1)=n^2$ and Its Connection to the Binary Goldbach Problem

Submission history