1. What is Pentagonal Edge Length of Pentagram?

The Pentagonal Edge Length of Pentagram refers to the edge length of the regular pentagon from which the Pentagram is constructed using its diagonals. It represents the side length of the underlying pentagonal shape.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( le(Pentagon) \) — Pentagonal Edge Length of Pentagram (m)
• \( lc \) — Chord Length of Pentagram (m)
• \( lLong\ Chord\ Slice \) — Long Chord Slice of Pentagram (m)

Explanation: This formula calculates the pentagonal edge length by subtracting the long chord slice from the total chord length of the pentagram.

3. Geometric Significance

Details: Understanding the relationship between chord length, long chord slice, and pentagonal edge length is essential in pentagram geometry and helps in constructing accurate pentagram shapes with precise proportions.

4. Using the Calculator

Tips: Enter chord length and long chord slice values in meters. Both values must be positive, and chord length must be greater than long chord slice for valid results.

5. Frequently Asked Questions (FAQ)

Q1: What is a pentagram?
A: A pentagram is a five-pointed star polygon formed by connecting the vertices of a regular pentagon with diagonals.

Q2: What is chord length in a pentagram?
A: Chord length refers to the diagonal length of the regular pentagon from which the pentagram is constructed.

Q3: What is long chord slice?
A: Long chord slice is the edge length of the entire star shape or the equal side of the isosceles triangle that forms the spike of the pentagram.

Q4: Can this formula be used for any pentagram?
A: This formula applies specifically to regular pentagrams constructed from regular pentagons with consistent proportions.

Q5: What are typical applications of this calculation?
A: This calculation is used in geometric design, architecture, sacred geometry, and mathematical studies of pentagram properties.