What is a Hypocycloid?
In geometry, a Hypocycloid is a special plane curve generated by the trace of a fixed point on a small circle that rolls within a larger circle. As the radius of the larger circle is increased, the Hypocycloid becomes more like the cycloid created by rolling a circle on a line.
Any Hypocycloid with an integral value of k, and thus k cusps, can move snugly inside another Hypocycloid with k+1 cusps, such that the points of the smaller Hypocycloid will always be in contact with the larger. This motion looks like 'rolling', though it is not technically rolling in the sense of classical mechanics, since it involves slipping.
How to Calculate Perimeter of Hypocycloid given Chord Length?
Perimeter of Hypocycloid given Chord Length calculator uses Perimeter of Hypocycloid = (4*Chord Length of Hypocycloid)/(sin(pi/Number of Cusps of Hypocycloid))*(Number of Cusps of Hypocycloid-1)/Number of Cusps of Hypocycloid to calculate the Perimeter of Hypocycloid, Perimeter of Hypocycloid given Chord Length is defined as the total length of all the boundary edges of the Hypocycloid, and calculated using the chord length of the Hypocycloid. Perimeter of Hypocycloid is denoted by P symbol.
How to calculate Perimeter of Hypocycloid given Chord Length using this online calculator? To use this online calculator for Perimeter of Hypocycloid given Chord Length, enter Chord Length of Hypocycloid (lc) & Number of Cusps of Hypocycloid (NCusps) and hit the calculate button. Here is how the Perimeter of Hypocycloid given Chord Length calculation can be explained with given input values -> 65.32998 = (4*12)/(sin(pi/5))*(5-1)/5.