Epitrochoid

epitrochoid spiralgraph

Mathematica Notebook for This Page epitrochoid_movies.nb.zip epitrochoid_movies2.nb.zip

History

See: Epicycloid and Hypocycloid.

Description

Epitrochoid is a family of cycloidal curves, a special case of Roulette. See Epicycloid and Hypocycloid for detail. Many famous curves are special cases of epitrochoid. (See: Curve Family Index).

epitrochoid epitrochoidGen
{1,2/3,.4}

Formula

See: Epicycloid and Hypocycloid.

Properties

Special Cases

h == 0, Circle.

b == h, epicycloids with q cusps, where q is the denominator of b written as a irreducible fraction.

a == b, limacon of Pascal. a == b == h, cardioid.

epitrochoidLimaconGen1
{1,1,3/5}
epitrochoidCardioidGen
{1,1,1}
epitrochoidLimaconGen2
{1,1,3}

a/2 == b == h, nephroid.

epitrochoidNephroidGen
{1,1/2,1/2}

Epitrochoid and Hypotrochoid Movie Gallery

Related Web Sites

See: Websites on Plane Curves, Plane Curves Books.

Robert Yates: Curves and Their Properties.

The MacTutor History of Mathematics archive

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Plane Curves

Ancient

  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

Cyclodal

  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

Methods

  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