Chord Length of Polygram Calculator

Chord Length of Polygram Formula:

\[ l_c = \sqrt{2 \times l_e^2 \times (1 - \cos(\angle_{outer}))} \]

Chord Length of Polygram:

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1. What is the Chord Length of Polygram?

The Chord Length of Polygram is the distance between any two adjacent spike tips of the Polygram from one tip to other tip. It represents the straight-line distance connecting two adjacent vertices of the polygram shape.

2. How Does the Calculator Work?

The calculator uses the Chord Length formula:

\[ l_c = \sqrt{2 \times l_e^2 \times (1 - \cos(\angle_{outer}))} \]

Where:

\( l_c \) — Chord Length of Polygram (m)
\( l_e \) — Edge Length of Polygram (m)
\( \angle_{outer} \) — Outer Angle of Polygram (rad)

Explanation: The formula calculates the chord length using trigonometric relationships between the edge length and the outer angle of the polygram.

3. Importance of Chord Length Calculation

Details: Calculating the chord length is essential for understanding the geometric properties of polygrams, designing polygram-based patterns, and solving geometric problems involving regular star polygons.

4. Using the Calculator

Tips: Enter the edge length in meters and the outer angle in radians. Both values must be positive numbers greater than zero.

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.

Q2: How is the outer angle defined?
A: The outer angle of a polygram is the angle between any two adjacent isosceles triangles which forms the spikes of the Polygram.

Q3: Can I use degrees instead of radians?
A: The calculator requires radians. Convert degrees to radians by multiplying by π/180.

Q4: What are typical values for polygram parameters?
A: Edge lengths can vary significantly depending on the specific polygram. Outer angles typically range between 0 and 2π radians.

Q5: Where are polygrams used in real life?
A: Polygrams appear in various fields including architecture, art, design patterns, and mathematical geometry studies.