VISUAL GEOMETRY: Generalized Fermat numbers:visual geometry

Generalized Fermat Numbers

https://oeis.org/wiki/Generalized_Fermat_numbers#:~:text=(...)-,Generalized%20Fermat%20numbers%20a%5E(2%5En)%20%2B,b%5E(2%5En)&text=1-,%7B3%2C%205%2C%2017%2C%20257%2C%2065537%2C%204294967297,%2C%20115792089237316195423570985008687907853269984665640564039457584007913129639937%2C%20...%7D

A way of visualizing the first generalized Fermat numbers using squares.

The numbers on those series get large very quickly and it becomes quite difficult to work on them on a visual basis after the first few numbers of each series.

Starting with a 3x3 square grid, for the series: 3,5,17,257,65537,4294967297,

https://oeis.org/A000215 ,

Fermat Numbers visualized: 3x3 square grid

3 , 5 Fermat numbers

One way of finding the next number in the series is to draw a square using G-N as a base and draw a perpendicular line to G-N that passes from the point L.

This will divide the G-N line into 1/5.

Repeat the same process with the new square , which is now a 5x5 square grid to get a new 17x17 square grid and so on.