Plane Curves

Ancient

  1. Conic Sections
  2. Parabola
  3. Hyperbola
  4. Ellipse
  1. Cissoid of Diocles
  2. Conchoid of Nicomedes
  3. Quadratrix Of Hippias

Spirals

  1. Archimedean Spiral
  2. Equiangular Spiral
  3. Lituus
  4. Cornu Spiral

Cyclodal Curves

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

Era of Calculus

  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

Era of Modern Math

  1. Sine Curve
  2. Catenary
  3. Bezier Curve

Methods of Generating New Curves

  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