Larger Radius of Hypocycloid given Smaller Radius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Larger Radius of Hypocycloid = Number of Cusps of Hypocycloid*Smaller Radius of Hypocycloid
rLarge = NCusps*rSmall
This formula uses 3 Variables
Variables Used
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.
Number of Cusps of Hypocycloid - Number of Cusps of Hypocycloid is the number of sharp tips or the round edged spikes of the Hypocycloid.
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
Number of Cusps of Hypocycloid: 5 --> No Conversion Required
Smaller Radius of Hypocycloid: 2 Meter --> 2 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rLarge = NCusps*rSmall --> 5*2
Evaluating ... ...
rLarge = 10
STEP 3: Convert Result to Output's Unit
10 Meter --> No Conversion Required
FINAL ANSWER
10 Meter <-- Larger Radius of Hypocycloid
(Calculation completed in 00.004 seconds)

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St Joseph's College (SJC), Bengaluru
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4 Radius of Large Circle of Hypocycloid Calculators

Larger Radius of Hypocycloid given Area
Go Larger Radius of Hypocycloid = Number of Cusps of Hypocycloid*sqrt(Area of Hypocycloid/(pi*(Number of Cusps of Hypocycloid-1)*(Number of Cusps of Hypocycloid-2)))
Larger Radius of Hypocycloid given Chord Length
Go Larger Radius of Hypocycloid = Chord Length of Hypocycloid/(2*sin(pi/Number of Cusps of Hypocycloid))
Larger Radius of Hypocycloid given Perimeter
Go Larger Radius of Hypocycloid = (Perimeter of Hypocycloid*Number of Cusps of Hypocycloid)/(8*(Number of Cusps of Hypocycloid-1))
Larger Radius of Hypocycloid given Smaller Radius
Go Larger Radius of Hypocycloid = Number of Cusps of Hypocycloid*Smaller Radius of Hypocycloid

Larger Radius of Hypocycloid given Smaller Radius Formula

Larger Radius of Hypocycloid = Number of Cusps of Hypocycloid*Smaller Radius of Hypocycloid
rLarge = NCusps*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 Larger Radius of Hypocycloid given Smaller Radius?

Larger Radius of Hypocycloid given Smaller Radius calculator uses Larger Radius of Hypocycloid = Number of Cusps of Hypocycloid*Smaller Radius of Hypocycloid to calculate the Larger Radius of Hypocycloid, Larger Radius of Hypocycloid given Smaller Radius formula is defined as the radius of the larger circle of Hypocycloid or the circle inside which the Hypocycloid shape is inscribed, and calculated using the radius of smaller circle of the Hypocycloid. Larger Radius of Hypocycloid is denoted by rLarge symbol.

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

FAQ

What is Larger Radius of Hypocycloid given Smaller Radius?
Larger Radius of Hypocycloid given Smaller Radius formula is defined as the radius of the larger circle of Hypocycloid or the circle inside which the Hypocycloid shape is inscribed, and calculated using the radius of smaller circle of the Hypocycloid and is represented as rLarge = NCusps*rSmall or Larger Radius of Hypocycloid = Number of Cusps of Hypocycloid*Smaller Radius of Hypocycloid. Number of Cusps of Hypocycloid is the number of sharp tips or the round edged spikes of the Hypocycloid & 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 Larger Radius of Hypocycloid given Smaller Radius?
Larger Radius of Hypocycloid given Smaller Radius formula is defined as the radius of the larger circle of Hypocycloid or the circle inside which the Hypocycloid shape is inscribed, and calculated using the radius of smaller circle of the Hypocycloid is calculated using Larger Radius of Hypocycloid = Number of Cusps of Hypocycloid*Smaller Radius of Hypocycloid. To calculate Larger Radius of Hypocycloid given Smaller Radius, you need Number of Cusps of Hypocycloid (NCusps) & Smaller Radius of Hypocycloid (rSmall). With our tool, you need to enter the respective value for Number of Cusps 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.
How many ways are there to calculate Larger Radius of Hypocycloid?
In this formula, Larger Radius of Hypocycloid uses Number of Cusps of Hypocycloid & Smaller Radius of Hypocycloid. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Larger Radius of Hypocycloid = Chord Length of Hypocycloid/(2*sin(pi/Number of Cusps of Hypocycloid))
  • Larger Radius of Hypocycloid = (Perimeter of Hypocycloid*Number of Cusps of Hypocycloid)/(8*(Number of Cusps of Hypocycloid-1))
  • Larger Radius of Hypocycloid = Number of Cusps of Hypocycloid*sqrt(Area of Hypocycloid/(pi*(Number of Cusps of Hypocycloid-1)*(Number of Cusps of Hypocycloid-2)))
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