Trisecting an Angle with a Limaçon

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The graph of a limaçon in polar coordinates is ; it can be constructed geometrically. Let be a ray with polar angle . Produce this line and determine point the so that . Then .


A limaçon with can be used to trisect angles. Choose the angle so that one leg intersects the limaçon at .

Since the triangle is isosceles, . Since the triangle is also isosceles, . So , or .


Contributed by: Izidor Hafner (September 2012)
Open content licensed under CC BY-NC-SA



Isaac Newton used a limaçon to trisect an angle.


[1] T. Iwamoto. "Trisection Using Special Curves." (Nov 22, 2006)

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