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Rolling a Polygon on a Circle
This Demonstration simulates a regular polygon rolling without slipping around a stationary base circle of radius 1.
The roulette traced by a point attached to the polygon consists of two different curve types:
1. involute curve sections when an edge of the polygon rolls tangentially over the base circle.
2. circle arcs when a vertex of the polygon makes contact with the base circle.
Varying the circumradius of the rolling polygon changes the circumference ratio
between the polygon and the base circle.
A closed curve can be obtained after one revolution around the base circle if the circumference of the
-sided regular polygon equals
.
By increasing the number of vertices of the polygon, the trace approaches an epitrochoid.
Contributed by:
Erik Mahieu
THINGS TO TRY
Slider Zoom
Gamepad Controls
Automatic Animation
SNAPSHOTS
RELATED LINKS
Roulette
(
Wolfram
MathWorld
)
Regular Polygon
(
Wolfram
MathWorld
)
Involute
(
Wolfram
MathWorld
)
Circle Involute
(
Wolfram
MathWorld
)
PERMANENT CITATION
Erik Mahieu
"
Rolling a Polygon on a Circle
"
http://demonstrations.wolfram.com/RollingAPolygonOnACircle/
Wolfram Demonstrations Project
Published: June 19, 2015
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