Edge Length of Polygram given Chord Length Calculator

Edge Length of Polygram Formula:

\[ l_e = \frac{l_c}{\sqrt{2 \times (1 - \cos(\theta_{\text{outer}}))}} \]

Edge Length of Polygram (l_e):

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1. What is the Edge Length of Polygram?

The Edge Length of Polygram is the length of any edge of the Polygram shape, from one end to other end. It's a fundamental measurement in polygram geometry that helps define the overall shape and proportions of the figure.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ l_e = \frac{l_c}{\sqrt{2 \times (1 - \cos(\theta_{\text{outer}}))}} \]

Where:

\( l_e \) — Edge Length of Polygram (m)
\( l_c \) — Chord Length of Polygram (m)
\( \theta_{\text{outer}} \) — Outer Angle of Polygram (radians)

Explanation: This formula calculates the edge length based on the chord length and the outer angle between adjacent isosceles triangles that form the polygram's spikes.

3. Importance of Edge Length Calculation

Details: Calculating the edge length is crucial for geometric construction, architectural design, and understanding the proportional relationships within polygram shapes. It helps determine the overall dimensions and symmetry of the figure.

4. Using the Calculator

Tips: Enter chord length in meters and outer angle in radians. Both values must be positive numbers. The calculator will compute the corresponding edge length of the polygram.

5. Frequently Asked Questions (FAQ)

Q1: What is a polygram?
A: A polygram is a star polygon formed by connecting non-adjacent vertices of a regular polygon, creating a star-shaped figure with spikes.

Q2: How is chord length different from edge length?
A: Chord length is the distance between adjacent spike tips, while edge length is the length of the actual sides that form the polygram's outline.

Q3: What units should I use for the angle?
A: The angle should be entered in radians. If you have degrees, convert them to radians first (radians = degrees × π/180).

Q4: Can this formula be used for all types of polygrams?
A: This specific formula applies to regular polygrams where the spikes are formed by isosceles triangles with equal outer angles.

Q5: What if I get a negative result?
A: Edge length should always be positive. If you get a negative result, check that your angle is within the valid range (typically between 0 and π radians).