WOLFRAM NOTEBOOK

WOLFRAM|DEMONSTRATIONS PROJECT

Roulette (Hypotrochogon) of a Polygon Rolling inside a Circle

​
number of vertices of polygon
n
3
4
5
6
7
8
radius of polygon circumcircle
r
0.366
pole offset from centroid
prolate hypotrochogon
pole at polygon centroid
pole at polygon vertex
number of traced sections
36
roll the polygon in the circle
ϕ
0.001
zoom control
2.5
show trace only
hide section markers
This Demonstration shows the roulette drawn by a point attached to a regular polygon rolling without slipping inside a circle.
This roulette curve is a sequence of circular arcs traced by the polygon when rolling along the edge of the circle.
For generalized cyclogons [1] and generalized trochoidal curves [2], these roulettes can be considered as limiting cases of hypotrochogons with an infinite number of vertices of the base (stationary) polygon.
Wolfram Cloud

You are using a browser not supported by the Wolfram Cloud

Supported browsers include recent versions of Chrome, Edge, Firefox and Safari.


I understand and wish to continue anyway »

You are using a browser not supported by the Wolfram Cloud. Supported browsers include recent versions of Chrome, Edge, Firefox and Safari.