trisectrix trisectrix
Artistic rendering of trisectrix's conchoids.

Mathematica Notebook for This Page.



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).

Constructing Trisectrix as a Conchoid



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.


Related Web Sites

See: Websites on Plane Curves, Plane Curves Books.

The MacTutor History of Mathematics archive

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Plane Curves


  1. Conic Sections
  2. Parabola
  3. Hyperbola
  4. Ellipse
  5. Cissoid
  6. Conchoid
  7. Quadratrix
  8. Archimedean Spiral
  9. Equiangular Spiral
  10. Lituus
  11. Cornu Spiral


  1. Epitrochoid
  2. Hypotrochoid
  3. Epicycloid and Hypocycloid
  4. Rose Curve
  5. Astroid
  6. Deltoid
  7. Nephroid
  8. Cardioid
  9. Trochoid
  10. Cycloid

Calculus Era

  1. Cassinian Oval
  2. Cross Curve
  3. Folium of Descartes
  4. Piriform
  5. Semicubic Parabola
  6. Tractrix
  7. Trisectrix
  8. Trisectrix of Maclaurin
  9. Lemniscate of Bernoulli
  10. Lemniscate of Gerono
  11. Limacon Of Pascal
  12. Witch of Agnesi
  13. Sine Curve
  14. Catenary
  15. Bezier Curve


  1. Caustics
  2. Cissoid
  3. Conchoid
  4. Envelope
  5. Evolute
  6. Involute
  7. Geometric Inversion
  8. Orthoptic
  9. Parallel Curve
  10. Pedal Curve
  11. Radial Curve
  12. Roulette

Math of Curves

  1. Geometry: Coordinate Systems for Plane Curves
  2. Coordinate Transformation
  3. Vectors
  4. Naming and Classification of Curves
  1. Cusp
  2. Curvature