Divide any circle by any prime number start with 11 and prove all segments are equal ,(no pi, radian or deg.)

Question

please no numerical solutions

Answer 1

There are only three prime numbers known, greater than 11, for which this division can be made and proved, using only a ruler and compass.

The numbers are 17, 257, and 65537.

The great Carl Friedrich Gauss (1777 - 1855) was the first to divide the circle into 17 parts, in 1796 when he was only 19 years old. He also proved that a circle could only be divided into N parts if every odd prime divisor of N was of the form 2^(2^n) + 1. The only known primes of this form are 3, 5, 17, 257 and 65537 for n = 0, 1, 2, 3 and 4.

F.J. Richelot divided the circle into 257 parts in 1832, and Professor Hermes of Lingen spent 10 years dividing it into 65537 parts, publishing the details in 1894.

Answer 2

How do you divide a circle, a geometric construct, by a prime number, a numerical construct......rephrase your concern

Answer 3

You probably should rephrase the question.

Generally, geometric figures can't be divided by numbers.

Answer 4

divide it into arcs, into areas, or what?

If you divide any shape into n equal parts then they are all equal, aren't they?

What exactly are you getting at?