Pythagoras Patchwork
- Author:
- Elliot 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?