Chryzodes

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

Chryzode

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.

If you can see this message, you do not have the Java software required to view the applet.













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