GXWeb Kissing Circles and Mathematical Bubbles
Channel: Compass Learning Technologies
Date: 2021-07-22

Imagine two circles - kissing! Now add a third and fourth circle to kiss both of these - each can only be placed in one of THREE positions, but could have many different sizes. Once the fourth kissing circle is added, however, everything changes! 

Kissing Circles take on a whole new look when they become bubbles in an Apollonian Gasket! Apollonios of Perga studied these mathematical bubbles in the third century BC, but it took a couple of modern mathematicians in the 1990s to show how, once again, Descartes Theorem can help to produce the coolest screensavers.

Explore the GXWeb Kissing Circles Collection:

The Kissing Circles Challenge: https://compasstech.com.au/gxwkisses/index.html

Descartes' Kissing Circles Theorem: https://compasstech.com.au/gxwdescartes/index.html

The Apollonian Gasket and Mathematical Bubbles: https://compasstech.com.au/gxwgasket/index.html

The Arbelos (The Shoemaker's Knife): https://compasstech.com.au/gxwarbelos/index.html

and the wonderful Farey Numbers and Ford Circles: https://compasstech.com.au/gxwfarey/index.html

All based upon the wonderful free, browser-based GXWeb software:

https://geometryexpressions.com/gxweb/

Explore more beautiful mathematics at the GXWeb Showcase:

https://compasstech.com.au/gx/index.html