Number of Cusps of Hypocycloid Solution

STEP 0: Pre-Calculation Summary
Formula Used
Number of Cusps of Hypocycloid = Larger Radius of Hypocycloid/Smaller Radius of Hypocycloid
NCusps = rLarge/rSmall
This formula uses 3 Variables
Variables Used
Number of Cusps of Hypocycloid - Number of Cusps of Hypocycloid is the number of sharp tips or the round edged spikes of the Hypocycloid.
Larger Radius of Hypocycloid - (Measured in Meter) - Larger Radius of Hypocycloid is the radius of the larger circle of Hypocycloid or the circle inside which the Hypocycloid shape is inscribed.
Smaller Radius of Hypocycloid - (Measured in Meter) - Smaller Radius of Hypocycloid is the radius of the circle which decides the number of cusps of the Hypocycloid and the width of portions cut from the larger circle to form the Hypocycloid.
STEP 1: Convert Input(s) to Base Unit
Larger Radius of Hypocycloid: 10 Meter --> 10 Meter No Conversion Required
Smaller Radius of Hypocycloid: 2 Meter --> 2 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
NCusps = rLarge/rSmall --> 10/2
Evaluating ... ...
NCusps = 5
STEP 3: Convert Result to Output's Unit
5 --> No Conversion Required
FINAL ANSWER
5 <-- Number of Cusps of Hypocycloid
(Calculation completed in 00.004 seconds)

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4 Area and Number of Cusps of Hypocycloid Calculators

Area of Hypocycloid given Chord Length
Go Area of Hypocycloid = pi*((Number of Cusps of Hypocycloid-1)*(Number of Cusps of Hypocycloid-2))/(Number of Cusps of Hypocycloid^2)*(Chord Length of Hypocycloid/(2*sin(pi/Number of Cusps of Hypocycloid)))^2
Area of Hypocycloid
Go Area of Hypocycloid = pi*((Number of Cusps of Hypocycloid-1)*(Number of Cusps of Hypocycloid-2))/(Number of Cusps of Hypocycloid^2)*Larger Radius of Hypocycloid^2
Area of Hypocycloid given Perimeter
Go Area of Hypocycloid = pi/64*(Number of Cusps of Hypocycloid-2)/(Number of Cusps of Hypocycloid-1)*Perimeter of Hypocycloid^2
Number of Cusps of Hypocycloid
Go Number of Cusps of Hypocycloid = Larger Radius of Hypocycloid/Smaller Radius of Hypocycloid

Number of Cusps of Hypocycloid Formula

Number of Cusps of Hypocycloid = Larger Radius of Hypocycloid/Smaller Radius of Hypocycloid
NCusps = rLarge/rSmall

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 Number of Cusps of Hypocycloid?

Number of Cusps of Hypocycloid calculator uses Number of Cusps of Hypocycloid = Larger Radius of Hypocycloid/Smaller Radius of Hypocycloid to calculate the Number of Cusps of Hypocycloid, Number of Cusps of Hypocycloid formula is defined as the number of sharp tips or the round edged spikes of the Hypocycloid. Number of Cusps of Hypocycloid is denoted by NCusps symbol.

How to calculate Number of Cusps of Hypocycloid using this online calculator? To use this online calculator for Number of Cusps of Hypocycloid, enter Larger Radius of Hypocycloid (rLarge) & Smaller Radius of Hypocycloid (rSmall) and hit the calculate button. Here is how the Number of Cusps of Hypocycloid calculation can be explained with given input values -> 5 = 10/2.

FAQ

What is Number of Cusps of Hypocycloid?
Number of Cusps of Hypocycloid formula is defined as the number of sharp tips or the round edged spikes of the Hypocycloid and is represented as NCusps = rLarge/rSmall or Number of Cusps of Hypocycloid = Larger Radius of Hypocycloid/Smaller Radius of Hypocycloid. Larger Radius of Hypocycloid is the radius of the larger circle of Hypocycloid or the circle inside which the Hypocycloid shape is inscribed & Smaller Radius of Hypocycloid is the radius of the circle which decides the number of cusps of the Hypocycloid and the width of portions cut from the larger circle to form the Hypocycloid.
How to calculate Number of Cusps of Hypocycloid?
Number of Cusps of Hypocycloid formula is defined as the number of sharp tips or the round edged spikes of the Hypocycloid is calculated using Number of Cusps of Hypocycloid = Larger Radius of Hypocycloid/Smaller Radius of Hypocycloid. To calculate Number of Cusps of Hypocycloid, you need Larger Radius of Hypocycloid (rLarge) & Smaller Radius of Hypocycloid (rSmall). With our tool, you need to enter the respective value for Larger Radius of Hypocycloid & Smaller Radius of Hypocycloid and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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