Vector in Octagon

sqrt(2) - sqrt(8 * (sin(22.5 degrees)^2) * (1 - cos(135 degrees)))
= 0

It shows that the length of the shortest diagonal line of an octagon inscribed in a circle with radius of 1 is square root of 2. How cosine formula and inner product work with vectors in octagon is demonstrated in my spreadsheet.

'Vector in Pentagon' was added to my spreadsheet to calculate magnitude of vector on the diagonal line of a pentagon which is a side of pentagon times phi. (06/11/25)