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Field: Number Theory
Image Created By: J-F. Collonna &. J-P Bourguigno
Website: Chryzode, the pictorial arithmetic


Chryzodes are visualizations of arithmetic using chords in a circle.

Basic Description

Chryzodes use a simple process to create beautiful images. Given a circle, a certain number of evenly spaced points are chosen on the perimeter of the circle. Each point represents a number. An operation, such as addition or multiplication, is then used to connect certain points.

For example, if multiplication by 2 is chosen, then the point representing 1 will be connected to the point representing 2, 2 to 4, 3 to 6, and so on. Notice that modular arithmetic is used here, so that  6*2=12 \equiv 5 \pmod {7}\ .

Continuing this process for a large number of iterations, creating many lines, produces images such as this page's main image. Below is an interactive applet which creates chryzodes based on user input.

ERROR: Unable to find Java Applet file: Chryzode.class.

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