Limaçon was used by
Blaise Pascal (1623 - 1662)
for Angle Trisection.
His idea is shown in the figure shown below.
In polar corrdinate: r = 2cos q + b
In rectangular coordinate: (x2 + y2 - 2x)2 = b2(x2 + y2)
Ð POA = Ð PAO and Ð OCP = Ð OPC = 2 x Ð PAO
Ð AOB = Ð PCO + Ð PAO = 3 x Ð PAO
Therefore Ð AOB is trisected.
******** limason_tri_desc.dwg ********
You can see the process in animation.
To create this drawing and animation:
Load Pascal.lsp (load "Pascal")
Then from command line, type pascal_5
All questions/suggestions should be sent to Takaya Iwamoto
Last Updated Nov 22, 2006
Copyright 2006 Takaya Iwamoto All rights reserved.