How to generate a hypocycloid

The animation shows how an hypocycloid is formed. A hypocycloid is "the curve produced by a fixed point P on the circumference of a circle with radius b rolling without sliding around the inside of a large circle of radius a, with a>b." (definition by: http://mathworld.wolfram.com/Hypocycloid.html) This dynamic interactive sheet has some problems: the angle B'O ̂B after having reached 359.99°, instead of keep growing, comes back to zero. For this it is impossible to close hypocycloids that need more than one rotation of the circumference β inside the circumference α cannot be drawn. It is also impossible to draw hypocycloids with the generating circumferences with a negative radius.

 

lasagni.francesco

 
Resource Type
Activity
Tags
ee  francesco  hypocycloid  lasagni 
Target Group (Age)
19+
Language
English (United Kingdom)
 
 
GeoGebra version
4.0
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5043
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