Chord Length of Pentagram Given Short Chord Slice Calculator

Formula Used:

\[ l_c = (2 \times l_{e(Pentagon)}) - l_{Short Chord Slice} \]

Chord Length of Pentagram:

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1. What is the Chord Length of Pentagram?

The Chord Length of Pentagram is the diagonal length of regular pentagon from which the Pentagram is constructed using its diagonals. It represents the distance between two non-adjacent vertices of the pentagram.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l_c = (2 \times l_{e(Pentagon)}) - l_{Short Chord Slice} \]

Where:

\( l_c \) — Chord Length of Pentagram (m)
\( l_{e(Pentagon)} \) — Pentagonal Edge Length of Pentagram (m)
\( l_{Short Chord Slice} \) — Short Chord Slice of Pentagram (m)

Explanation: This formula calculates the chord length by doubling the pentagonal edge length and subtracting the short chord slice value.

3. Importance of Chord Length Calculation

Details: Calculating the chord length of a pentagram is important in geometric design, architectural planning, and mathematical studies of pentagonal symmetry. It helps in understanding the proportional relationships within pentagram structures.

4. Using the Calculator

Tips: Enter the pentagonal edge length and short chord slice values in meters. Both values must be positive numbers greater than zero for accurate calculation.

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 pentagon with straight lines.

Q2: How is the chord length related to the pentagon edges?
A: The chord length represents the diagonal distance between non-adjacent vertices and is derived from the pentagon's edge measurements.

Q3: Can this formula be used for any pentagram?
A: This formula applies specifically to regular pentagrams constructed from regular pentagons where all sides and angles are equal.

Q4: What units should I use for the inputs?
A: The calculator uses meters as the default unit, but any consistent unit of length can be used as long as both inputs are in the same unit.

Q5: What if I get a negative result?
A: A negative result indicates that the short chord slice value is larger than twice the pentagonal edge length, which is geometrically impossible for a valid pentagram. Please verify your input values.