Chord Length of Hypocycloid given Area 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%
✖Area of Hypocycloid is the total quantity of plane enclosed by the boundary of the Hypocycloid.ⓘ Area of Hypocycloid [A]			+10% -10%

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

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Chord Length of Hypocycloid given Area

Formula

`"l"_{"c"} = 2*sin(pi/"N"_{"Cusps"})*"N"_{"Cusps"}*sqrt("A"/(pi*("N"_{"Cusps"}-1)*("N"_{"Cusps"}-2)))`

Example

`"11.72462m"=2*sin(pi/"5")*"5"*sqrt("150m²"/(pi*("5"-1)*("5"-2)))`

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Chord Length of Hypocycloid given Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
l_c = 2*sin(pi/N_Cusps)*N_Cusps*sqrt(A/(pi*(N_Cusps-1)*(N_Cusps-2)))
This formula uses 1 Constants, 2 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)
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

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.
Area of Hypocycloid - (Measured in Square Meter) - Area of Hypocycloid is the total quantity of plane enclosed by the boundary of the Hypocycloid.

STEP 1: Convert Input(s) to Base Unit

Number of Cusps of Hypocycloid: 5 --> No Conversion Required
Area of Hypocycloid: 150 Square Meter --> 150 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_c = 2*sin(pi/N_Cusps)*N_Cusps*sqrt(A/(pi*(N_Cusps-1)*(N_Cusps-2))) --> 2*sin(pi/5)*5*sqrt(150/(pi*(5-1)*(5-2)))

Evaluating ... ...

l_c = 11.7246194467945

STEP 3: Convert Result to Output's Unit

11.7246194467945 Meter --> No Conversion Required

FINAL ANSWER

11.7246194467945 ≈ 11.72462 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 Area 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 Area?

Chord Length of Hypocycloid given Area calculator uses 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))) to calculate the Chord Length of Hypocycloid, Chord Length of Hypocycloid given Area formula is defined as the linear distance between any two adjacent cusps of the Hypocycloid, and calculated using the area of the Hypocycloid. Chord Length of Hypocycloid is denoted by l_c symbol.

How to calculate Chord Length of Hypocycloid given Area using this online calculator? To use this online calculator for Chord Length of Hypocycloid given Area, enter Number of Cusps of Hypocycloid (N_Cusps) & Area of Hypocycloid (A) and hit the calculate button. Here is how the Chord Length of Hypocycloid given Area calculation can be explained with given input values -> 11.72462 = 2*sin(pi/5)*5*sqrt(150/(pi*(5-1)*(5-2))).

FAQ

What is Chord Length of Hypocycloid given Area?

Chord Length of Hypocycloid given Area formula is defined as the linear distance between any two adjacent cusps of the Hypocycloid, and calculated using the area of the Hypocycloid and is represented as l_c = 2*sin(pi/N_Cusps)*N_Cusps*sqrt(A/(pi*(N_Cusps-1)*(N_Cusps-2))) or 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))). Number of Cusps of Hypocycloid is the number of sharp tips or the round edged spikes of the Hypocycloid & Area of Hypocycloid is the total quantity of plane enclosed by the boundary of the Hypocycloid.

How to calculate Chord Length of Hypocycloid given Area?

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

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