Special Curves

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Trisecting an Angle
Special Curves

### Trisection using Special Curves

#### Limaçon- by Pascal

Limaçon was used by
Blaise Pascal (1623 - 1662)
for Angle Trisection.

His idea is shown in the figure shown below.

##### Equation of the curve

In polar corrdinate: **r = 2cos q + b**

In rectangular coordinate: **(x**^{2} + y^{2} - 2x)^{2} = b^{2}(x^{2} + y^{2})

##### Angle Trisection

Since Triangles COP and POA are isosceles,
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 **

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Special Curves

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Last Updated Nov 22, 2006

Copyright 2006 Takaya Iwamoto All rights reserved.
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