Chord Length of Hypocycloid given Perimeter Calculator

✖Number of Cusps of Hypocycloid is the number of sharp tips or the round edged spikes of the Hypocycloid.ⓘ Number of Cusps of Hypocycloid [N_Cusps]			+10% -10%
✖Perimeter of Hypocycloid is the total length of all the boundary edges of the Hypocycloid.ⓘ Perimeter of Hypocycloid [P]			+10% -10%

✖Chord Length of Hypocycloid is the linear distance between any two adjacent cusps of the Hypocycloid.ⓘ Chord Length of Hypocycloid given Perimeter [l_c]

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Formula

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Chord Length of Hypocycloid given Perimeter

Formula

`"l"_{"c"} = sin(pi/"N"_{"Cusps"})*("P"*"N"_{"Cusps"})/(4*("N"_{"Cusps"}-1))`

Example

`"11.93939m"=sin(pi/"5")*("65m"*"5")/(4*("5"-1))`

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Chord Length of Hypocycloid given Perimeter Solution

STEP 0: Pre-Calculation Summary

Formula Used

Chord Length of Hypocycloid = sin(pi/Number of Cusps of Hypocycloid)*(Perimeter of Hypocycloid*Number of Cusps of Hypocycloid)/(4*(Number of Cusps of Hypocycloid-1))
l_c = sin(pi/N_Cusps)*(P*N_Cusps)/(4*(N_Cusps-1))
This formula uses 1 Constants, 1 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)

Variables Used

Chord Length of Hypocycloid - (Measured in Meter) - Chord Length of Hypocycloid is the linear distance between any two adjacent cusps of the Hypocycloid.
Number of Cusps of Hypocycloid - Number of Cusps of Hypocycloid is the number of sharp tips or the round edged spikes of the Hypocycloid.
Perimeter of Hypocycloid - (Measured in Meter) - Perimeter of Hypocycloid is the total length of all the boundary edges of the Hypocycloid.

STEP 1: Convert Input(s) to Base Unit

Number of Cusps of Hypocycloid: 5 --> No Conversion Required
Perimeter of Hypocycloid: 65 Meter --> 65 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_c = sin(pi/N_Cusps)*(P*N_Cusps)/(4*(N_Cusps-1)) --> sin(pi/5)*(65*5)/(4*(5-1))

Evaluating ... ...

l_c = 11.9393879371909

STEP 3: Convert Result to Output's Unit

11.9393879371909 Meter --> No Conversion Required

FINAL ANSWER

11.9393879371909 ≈ 11.93939 Meter <-- Chord Length of Hypocycloid

(Calculation completed in 00.004 seconds)

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< 3 Chord Length of Hypocycloid Calculators

Chord Length of Hypocycloid given Area

Go Chord Length of Hypocycloid = 2*sin(pi/Number of Cusps of Hypocycloid)*Number of Cusps of Hypocycloid*sqrt(Area of Hypocycloid/(pi*(Number of Cusps of Hypocycloid-1)*(Number of Cusps of Hypocycloid-2)))

Chord Length of Hypocycloid given Perimeter

Go Chord Length of Hypocycloid = sin(pi/Number of Cusps of Hypocycloid)*(Perimeter of Hypocycloid*Number of Cusps of Hypocycloid)/(4*(Number of Cusps of Hypocycloid-1))

Chord Length of Hypocycloid

Go Chord Length of Hypocycloid = 2*sin(pi/Number of Cusps of Hypocycloid)*Larger Radius of Hypocycloid

Chord Length of Hypocycloid given Perimeter Formula

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 Chord Length of Hypocycloid given Perimeter?

Chord Length of Hypocycloid given Perimeter calculator uses Chord Length of Hypocycloid = sin(pi/Number of Cusps of Hypocycloid)*(Perimeter of Hypocycloid*Number of Cusps of Hypocycloid)/(4*(Number of Cusps of Hypocycloid-1)) to calculate the Chord Length of Hypocycloid, Chord Length of Hypocycloid given Perimeter is defined as the linear distance between any two adjacent cusps of the Hypocycloid, and calculated using the perimeter of the Hypocycloid. Chord Length of Hypocycloid is denoted by l_c symbol.

How to calculate Chord Length of Hypocycloid given Perimeter using this online calculator? To use this online calculator for Chord Length of Hypocycloid given Perimeter, enter Number of Cusps of Hypocycloid (N_Cusps) & Perimeter of Hypocycloid (P) and hit the calculate button. Here is how the Chord Length of Hypocycloid given Perimeter calculation can be explained with given input values -> 11.93939 = sin(pi/5)*(65*5)/(4*(5-1)).

FAQ

What is Chord Length of Hypocycloid given Perimeter?

Chord Length of Hypocycloid given Perimeter is defined as the linear distance between any two adjacent cusps of the Hypocycloid, and calculated using the perimeter of the Hypocycloid and is represented as l_c = sin(pi/N_Cusps)*(P*N_Cusps)/(4*(N_Cusps-1)) or Chord Length of Hypocycloid = sin(pi/Number of Cusps of Hypocycloid)*(Perimeter of Hypocycloid*Number of Cusps of Hypocycloid)/(4*(Number of Cusps of Hypocycloid-1)). Number of Cusps of Hypocycloid is the number of sharp tips or the round edged spikes of the Hypocycloid & Perimeter of Hypocycloid is the total length of all the boundary edges of the Hypocycloid.

How to calculate Chord Length of Hypocycloid given Perimeter?

Chord Length of Hypocycloid given Perimeter is defined as the linear distance between any two adjacent cusps of the Hypocycloid, and calculated using the perimeter of the Hypocycloid is calculated using Chord Length of Hypocycloid = sin(pi/Number of Cusps of Hypocycloid)*(Perimeter of Hypocycloid*Number of Cusps of Hypocycloid)/(4*(Number of Cusps of Hypocycloid-1)). To calculate Chord Length of Hypocycloid given Perimeter, you need Number of Cusps of Hypocycloid (N_Cusps) & Perimeter of Hypocycloid (P). With our tool, you need to enter the respective value for Number of Cusps of Hypocycloid & Perimeter 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 Chord Length of Hypocycloid?

In this formula, Chord Length of Hypocycloid uses Number of Cusps of Hypocycloid & Perimeter of Hypocycloid. We can use 2 other way(s) to calculate the same, which is/are as follows -

Chord Length of Hypocycloid = 2*sin(pi/Number of Cusps of Hypocycloid)*Larger Radius of Hypocycloid
Chord Length of Hypocycloid = 2*sin(pi/Number of Cusps 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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