This page is a sub-page of our page on Plane Curves.
///////
Related KMR-pages:
• The Brachistochrone (= The curve of quickest descent)
• The Tautochrone (= The curve of equal descent)
///////
Other relevant sources of information:
• Cycloids at Wikipedia
• Trochoids at Wikipedia
• Trochoids at Wolfram MathWorld
• Epicycloids at Wikipedia
• Epitrochoids at Wikipedia
• Hypocycloids at Wikipedia
• Hypotrochoids at Wikipedia
• History of the Cycloid at Wikipedia
• The mathematics of the Epicycloid – A historical journey with a modern perspective
• Cycloidal curves
• Trochoidal Wave
• Deferents and epicycles at Wikipedia
• Joe Freedman’s Amazing Cycloid Drawing Machine
///////
The interactive simulations on this page can be navigated with the Free Viewer
of the Graphing Calculator.
///////
Cycloid and Trochoid – orbits:
The interactive simulation that generated this movie.
Drag the blue point at the bottom horizontally to change the Trochoid.
///////
The interactive simulation that created this movie.
///////
CycloidEvolute – Involutes:
/////////////////////// THE MOVIE IS MISSING
The interactive simulation that will create this movie.
///////
An interactive simulation of Epicycloids and Hypocycloids.
Drag the blue point horizontally to change between epicycloid (= the blue point to the left of the green point) and hypocycloid (= the blue point to the right of the green point).
The horizontal position of the green point controls the radius of the moving circle.
///////
////////
////////
////////
////////
////////
The interactive simulation that created these movies.
///////
///////
///////
///////
///////
///////
///////
///////
The interactive simulation that created these movies.
///////
///////
Epitrochoid Flash Animation (Sergio Flores Morales on YouTube):
///////
Luxor hypotrochoids alternative take (C ormullion on YouTube):
///////