Pappus Chain
1,861 views · Published 24 July 2008 · 0:17 · Indexed 8 November 2026
Channel: Wolfram · 2008 · Education
http://demonstrations.wolfram.com/PappusChain/ The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily. The Pappus chain extends across at least two millennia of mathematics. Its origins trace back to the ancient Greek mathematician Archimedes and his studies of circles inscribed within the figure of an arbelos (or shoemaker's knife). The inversive geometry trick for efficiently computing the positions of pairwise tangent inscribed circles, or a Pappus chain, is apparently a modern invention. The Apollonian gasket or curvilinear Sierpinski sieve is constructed by the same iterative process of inscribing a circle in triplets of tangent circles. Thus the Pappus chain construction anticipates the class-2 nested behavior of many elementary cellular automata. By Christopher Haydock (Applied New Science LLC)
More from this channel
-
2:37
Positioned for Success: Targeting Mathematica to Strengthen U.S. Defense
-
3:44
Prescription for Savings: Mathematica Powers Efficiency in Drug Trials
-
3:10
Eye on Cancer Prevention: Precision in Cancer Diagnosis with Mathematica
-
3:32
Power of Prescreening: Mathematica Saves Time and Money in Prescreening
-
2:47
Breaking Down Biofuels: Green Solutions with Mathematica
-
2:58
Efficient Coding Takes Off: Flight Simulation with Mathematica
-
2:21
Striking a Virtual Chord: Mathematica Hits High Note with Music Producer
-
0:54
International Mathematica User Conference 2008