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 Area of Hypocycloid given Perimeter?
Area of Hypocycloid given Perimeter calculator uses Area of Hypocycloid = pi/64*(Number of Cusps of Hypocycloid-2)/(Number of Cusps of Hypocycloid-1)*Perimeter of Hypocycloid^2 to calculate the Area of Hypocycloid, Area of Hypocycloid given Perimeter formula is defined as the total quantity of plane enclosed by the boundary of the Hypocycloid, and calculated using the perimeter of the Hypocycloid. Area of Hypocycloid is denoted by A symbol.
How to calculate Area of Hypocycloid given Perimeter using this online calculator? To use this online calculator for Area of Hypocycloid given Perimeter, enter Number of Cusps of Hypocycloid (NCusps) & Perimeter of Hypocycloid (P) and hit the calculate button. Here is how the Area of Hypocycloid given Perimeter calculation can be explained with given input values -> 155.5457 = pi/64*(5-2)/(5-1)*65^2.