Number of Spikes in Polygram given Outer and Inner Angles Calculator

✖The Outer Angle of Polygram is the angle between any two adjacent isosceles triangles which forms the spikes of the Polygram.ⓘ Outer Angle of Polygram [∠_Outer]			+10% -10%
✖The Inner Angle of Polygram is the unequal angle of the isosceles triangle which forms the spikes of the Polygram or the angle inside the tip of any spike of Polygram.ⓘ Inner Angle of Polygram [∠_Inner]			+10% -10%

✖The Number of Spikes in Polygram is the total count of isosceles triangular spikes the Polygram has or the total number of sides of the polygon on which the spikes are attached to form the Polygram.ⓘ Number of Spikes in Polygram given Outer and Inner Angles [N_Spikes]

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Formula

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Number of Spikes in Polygram given Outer and Inner Angles

Formula

`"N"_{"Spikes"} = (2*pi)/("∠"_{"Outer"}-"∠"_{"Inner"})`

Example

`"10"=(2*pi)/("110°"-"74°")`

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Number of Spikes in Polygram given Outer and Inner Angles Solution

STEP 0: Pre-Calculation Summary

Formula Used

Number of Spikes in Polygram = (2*pi)/(Outer Angle of Polygram-Inner Angle of Polygram)
N_Spikes = (2*pi)/(∠_Outer-∠_Inner)
This formula uses 1 Constants, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Number of Spikes in Polygram - The Number of Spikes in Polygram is the total count of isosceles triangular spikes the Polygram has or the total number of sides of the polygon on which the spikes are attached to form the Polygram.
Outer Angle of Polygram - (Measured in Radian) - The Outer Angle of Polygram is the angle between any two adjacent isosceles triangles which forms the spikes of the Polygram.
Inner Angle of Polygram - (Measured in Radian) - The Inner Angle of Polygram is the unequal angle of the isosceles triangle which forms the spikes of the Polygram or the angle inside the tip of any spike of Polygram.

STEP 1: Convert Input(s) to Base Unit

Outer Angle of Polygram: 110 Degree --> 1.9198621771934 Radian (Check conversion here)
Inner Angle of Polygram: 74 Degree --> 1.29154364647556 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

N_Spikes = (2*pi)/(∠_Outer-∠_Inner) --> (2*pi)/(1.9198621771934-1.29154364647556)

Evaluating ... ...

N_Spikes = 10.0000000000019

STEP 3: Convert Result to Output's Unit

10.0000000000019 --> No Conversion Required

FINAL ANSWER

10.0000000000019 ≈ 10 <-- Number of Spikes in Polygram

(Calculation completed in 00.004 seconds)

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Created by Jaseem K

IIT Madras (IIT Madras), Chennai

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< 2 Number of Points of Polygram Calculators

Number of Spikes in Polygram given Outer and Inner Angles

Go Number of Spikes in Polygram = (2*pi)/(Outer Angle of Polygram-Inner Angle of Polygram)

Number of Spikes in Polygram given Perimeter

Go Number of Spikes in Polygram = Perimeter of Polygram/(2*Edge Length of Polygram)

Number of Spikes in Polygram given Outer and Inner Angles Formula

Number of Spikes in Polygram = (2*pi)/(Outer Angle of Polygram-Inner Angle of Polygram)
N_Spikes = (2*pi)/(∠_Outer-∠_Inner)

What is Polygram ?

A Polygram is a regular n-sided polygon with identical isosceles triangles (also known as SPIKES) attached to each edge. It looks like an n-pointed star. For an n-pointed star, there will be n-spikes. The Spike (Isosceles Triangle) is an important part of the polygram and it is defined using 4 parameters. They are : 1) The Base Length of the Triangle (Base Length of the Polygram) 2) Length of the equal side of the triangle (Edge Length of the Polygram) 3) Angle between the two equal sides of the isosceles triangle (Inner Angle angle of the Polygram) 4) Height of the triangle (Spike Height) Apart from these, there are other important parameters that define the Polygram. They are: 1) Outer Angle: The angle between two adjacent isosceles triangles. 2) Chord Length: The distance between two peaks of the adjacent Spikes of the Polygram. 3) Perimeter: The sum of lengths of all the edges of the polygram. 4) Area : The amount of space occupied by the polygram.

How to Calculate Number of Spikes in Polygram given Outer and Inner Angles?

Number of Spikes in Polygram given Outer and Inner Angles calculator uses Number of Spikes in Polygram = (2*pi)/(Outer Angle of Polygram-Inner Angle of Polygram) to calculate the Number of Spikes in Polygram, The Number of Spikes in Polygram given Outer and Inner Angles formula is defined as the number of triangular extensions that a Polygram has, and calculated using the outer and inner angles. Number of Spikes in Polygram is denoted by N_Spikes symbol.

How to calculate Number of Spikes in Polygram given Outer and Inner Angles using this online calculator? To use this online calculator for Number of Spikes in Polygram given Outer and Inner Angles, enter Outer Angle of Polygram (∠_Outer) & Inner Angle of Polygram (∠_Inner) and hit the calculate button. Here is how the Number of Spikes in Polygram given Outer and Inner Angles calculation can be explained with given input values -> 10 = (2*pi)/(1.9198621771934-1.29154364647556).

FAQ

What is Number of Spikes in Polygram given Outer and Inner Angles?

The Number of Spikes in Polygram given Outer and Inner Angles formula is defined as the number of triangular extensions that a Polygram has, and calculated using the outer and inner angles and is represented as N_Spikes = (2*pi)/(∠_Outer-∠_Inner) or Number of Spikes in Polygram = (2*pi)/(Outer Angle of Polygram-Inner Angle of Polygram). The Outer Angle of Polygram is the angle between any two adjacent isosceles triangles which forms the spikes of the Polygram & The Inner Angle of Polygram is the unequal angle of the isosceles triangle which forms the spikes of the Polygram or the angle inside the tip of any spike of Polygram.

How to calculate Number of Spikes in Polygram given Outer and Inner Angles?

The Number of Spikes in Polygram given Outer and Inner Angles formula is defined as the number of triangular extensions that a Polygram has, and calculated using the outer and inner angles is calculated using Number of Spikes in Polygram = (2*pi)/(Outer Angle of Polygram-Inner Angle of Polygram). To calculate Number of Spikes in Polygram given Outer and Inner Angles, you need Outer Angle of Polygram (∠_Outer) & Inner Angle of Polygram (∠_Inner). With our tool, you need to enter the respective value for Outer Angle of Polygram & Inner Angle of Polygram 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 Number of Spikes in Polygram?

In this formula, Number of Spikes in Polygram uses Outer Angle of Polygram & Inner Angle of Polygram. We can use 1 other way(s) to calculate the same, which is/are as follows -

Number of Spikes in Polygram = Perimeter of Polygram/(2*Edge Length of Polygram)

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