Perimeter of Hypocycloid given Chord Length Solution

STEP 0: Pre-Calculation Summary
Formula Used
Perimeter of Hypocycloid = (4*Chord Length of Hypocycloid)/(sin(pi/Number of Cusps of Hypocycloid))*(Number of Cusps of Hypocycloid-1)/Number of Cusps of Hypocycloid
P = (4*lc)/(sin(pi/NCusps))*(NCusps-1)/NCusps
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
Perimeter of Hypocycloid - (Measured in Meter) - Perimeter of Hypocycloid is the total length of all the boundary edges of the Hypocycloid.
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.
STEP 1: Convert Input(s) to Base Unit
Chord Length of Hypocycloid: 12 Meter --> 12 Meter No Conversion Required
Number of Cusps of Hypocycloid: 5 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
P = (4*lc)/(sin(pi/NCusps))*(NCusps-1)/NCusps --> (4*12)/(sin(pi/5))*(5-1)/5
Evaluating ... ...
P = 65.3299820814367
STEP 3: Convert Result to Output's Unit
65.3299820814367 Meter --> No Conversion Required
FINAL ANSWER
65.3299820814367 65.32998 Meter <-- Perimeter of Hypocycloid
(Calculation completed in 00.006 seconds)

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Perimeter of Hypocycloid Calculators

Perimeter of Hypocycloid given Chord Length
​ LaTeX ​ Go Perimeter of Hypocycloid = (4*Chord Length of Hypocycloid)/(sin(pi/Number of Cusps of Hypocycloid))*(Number of Cusps of Hypocycloid-1)/Number of Cusps of Hypocycloid
Perimeter of Hypocycloid given Area
​ LaTeX ​ Go Perimeter of Hypocycloid = 8*sqrt((Area of Hypocycloid*(Number of Cusps of Hypocycloid-1))/(pi*(Number of Cusps of Hypocycloid-2)))
Perimeter of Hypocycloid
​ LaTeX ​ Go Perimeter of Hypocycloid = (8*Larger Radius of Hypocycloid*(Number of Cusps of Hypocycloid-1))/Number of Cusps of Hypocycloid

Perimeter of Hypocycloid given Chord Length Formula

​LaTeX ​Go
Perimeter of Hypocycloid = (4*Chord Length of Hypocycloid)/(sin(pi/Number of Cusps of Hypocycloid))*(Number of Cusps of Hypocycloid-1)/Number of Cusps of Hypocycloid
P = (4*lc)/(sin(pi/NCusps))*(NCusps-1)/NCusps

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 Perimeter of Hypocycloid given Chord Length?

Perimeter of Hypocycloid given Chord Length calculator uses Perimeter of Hypocycloid = (4*Chord Length of Hypocycloid)/(sin(pi/Number of Cusps of Hypocycloid))*(Number of Cusps of Hypocycloid-1)/Number of Cusps of Hypocycloid to calculate the Perimeter of Hypocycloid, Perimeter of Hypocycloid given Chord Length is defined as the total length of all the boundary edges of the Hypocycloid, and calculated using the chord length of the Hypocycloid. Perimeter of Hypocycloid is denoted by P symbol.

How to calculate Perimeter of Hypocycloid given Chord Length using this online calculator? To use this online calculator for Perimeter of Hypocycloid given Chord Length, enter Chord Length of Hypocycloid (lc) & Number of Cusps of Hypocycloid (NCusps) and hit the calculate button. Here is how the Perimeter of Hypocycloid given Chord Length calculation can be explained with given input values -> 65.32998 = (4*12)/(sin(pi/5))*(5-1)/5.

FAQ

What is Perimeter of Hypocycloid given Chord Length?
Perimeter of Hypocycloid given Chord Length is defined as the total length of all the boundary edges of the Hypocycloid, and calculated using the chord length of the Hypocycloid and is represented as P = (4*lc)/(sin(pi/NCusps))*(NCusps-1)/NCusps or Perimeter of Hypocycloid = (4*Chord Length of Hypocycloid)/(sin(pi/Number of Cusps of Hypocycloid))*(Number of Cusps of Hypocycloid-1)/Number of Cusps of Hypocycloid. Chord Length of Hypocycloid is the linear distance between any two adjacent cusps of the Hypocycloid & Number of Cusps of Hypocycloid is the number of sharp tips or the round edged spikes of the Hypocycloid.
How to calculate Perimeter of Hypocycloid given Chord Length?
Perimeter of Hypocycloid given Chord Length is defined as the total length of all the boundary edges of the Hypocycloid, and calculated using the chord length of the Hypocycloid is calculated using Perimeter of Hypocycloid = (4*Chord Length of Hypocycloid)/(sin(pi/Number of Cusps of Hypocycloid))*(Number of Cusps of Hypocycloid-1)/Number of Cusps of Hypocycloid. To calculate Perimeter of Hypocycloid given Chord Length, you need Chord Length of Hypocycloid (lc) & Number of Cusps of Hypocycloid (NCusps). With our tool, you need to enter the respective value for Chord Length of Hypocycloid & Number of Cusps 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 Perimeter of Hypocycloid?
In this formula, Perimeter of Hypocycloid uses Chord Length of Hypocycloid & Number of Cusps of Hypocycloid. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Perimeter of Hypocycloid = (8*Larger Radius of Hypocycloid*(Number of Cusps of Hypocycloid-1))/Number of Cusps of Hypocycloid
  • Perimeter of Hypocycloid = 8*sqrt((Area of Hypocycloid*(Number of Cusps of Hypocycloid-1))/(pi*(Number of Cusps of Hypocycloid-2)))
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