## Interactive and animated Geometric Algebra with Cinderella

- Clifford's circle chain theorem

Clifford's circle chain theorem in the ordinary Euclidean plane refers to a "chain of theorems" of increasing complexity.
Every one of this infinite sequence of theorems must be true for the whole to be true. It begins with two circles passing
through a common point O (n=2). The next theorem in the chain is for the case of three circles through a common point O (n=3)
and so forth for n=4,5,6, ... If one takes the point O to infinity the n circles become n straight lines
(circles with infinite radii.) The following shows interactive diagrams for the cases n=2, ... ,8 circles through O.

**Reference**

R. Penrose *The Mathematics of William Kingdon Clifford: A Personal Reflection*,
in M. Chisholm *Such Silver Currents - The Story of William and Lucy Clifford 1845-1929*,
Lutterworth, Cambridge 2002.

[ GA
with Cinderella
| vectors
| outer prod.
| triangle
| rotations
| oscillations
| circ. pol. waves
| conics
| struc. mechanics
| 2D point groups
]

Soli Deo Gloria. Created with Cinderella by Eckhard Hitzer (Fukui).