Trisectrix

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Artistic rendering of trisectrix's conchoids.

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History

Description

Trisectrix is a general name for curves that can be used to trisect a angle. The name trisectrix is often reserved for a special case of limacon of Pascal, which we discuss here. Other famous trisectrix include trisectrix of Maclaurin and conchoid of Nicomedes.

Trisectrix can be generated as a conchoid or epitrochoid. (See: limacon of Pascal for definition).

trisectrix
Constructing Trisectrix as a Conchoid

Formula

Properties

Trisecting a Angle

Let P be any point on the outer loop of the curve. The angle formed by P, {1,0}, {3,0} is three times larger than the angle {0,0}, P, {1,0}.

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Trisecting a Angle

Graphic Gallery

Parallels of trisectrix.

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Normals and osculating circles of a trisectrix. Note that the evolute of trisectrix is NOT nephroid.
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Conchoids of trisectrix.
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Various Conchoid of trisectrix
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Conchoid of trisectrix with a moving point 1.
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String art based on trisectrix.

trisectrix.pdf

Related Web Sites

See: Websites on Plane Curves, Printed References On Plane Curves.

The MacTutor History of Mathematics archive

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