# Pythagoras Patchwork

- Author:
- Mr Malkin

(The app may take a few seconds to load.)

Each integer coordinate is shaded depending upon the remainder when is divided by , with greater remainders given darker shading.
Use the blue slider to change the value of , or press "Play/Stop".
Use the checkbox to highlight when a remainder of is given (i.e. when is a multiple of ).
Some questions:

- What are the symmetries of the patterns?
- Which values of
give the greatest numbers of zeros? (Why does give so many but so few?) - Why do circles form, and what is happening in between the circles?