Edge Length of Polygram given Base Length Calculator

Edge Length of Polygram Formula:

\[ l_e = \frac{l_{Base}}{\sqrt{2 \times (1 - \cos(\angle_{Inner}))}} \]

Edge Length of Polygram:

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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 is an important geometric measurement in polygram construction and analysis.

2. How Does the Calculator Work?

The calculator uses the Edge Length of Polygram formula:

\[ l_e = \frac{l_{Base}}{\sqrt{2 \times (1 - \cos(\angle_{Inner}))}} \]

Where:

\( l_e \) — Edge Length of Polygram (m)
\( l_{Base} \) — Base Length of Polygram (m)
\( \angle_{Inner} \) — Inner Angle of Polygram (rad)

Explanation: The formula calculates the edge length based on the base length and inner angle using trigonometric relationships and square root functions.

3. Importance of Edge Length Calculation

Details: Accurate edge length calculation is crucial for geometric construction, architectural design, and mathematical analysis of polygram shapes and patterns.

4. Using the Calculator

Tips: Enter base length in meters, inner angle in radians. All values must be valid positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a Polygram?
A: A polygram is a geometric figure consisting of multiple intersecting lines that form a star-like pattern.

Q2: How is the inner angle measured?
A: The inner angle is the angle inside the tip of any spike of the polygram, measured in radians.

Q3: Can this calculator handle different units?
A: The calculator uses meters for length and radians for angles. Convert other units accordingly before calculation.

Q4: What if I get an error in calculation?
A: Ensure all input values are positive numbers and the inner angle is within valid trigonometric range.

Q5: Are there limitations to this formula?
A: The formula assumes standard polygram geometry and may not apply to irregular or modified polygram shapes.