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The Short Chord Slice of Pentagram is the edge length of the regular pentagon which forms inside the Pentagram when all the chords are drawn. It represents one of the fundamental geometric relationships in pentagram construction.
The calculator uses the formula:
Where:
Explanation: This formula demonstrates the fundamental relationship between the long and short chord slices in a pentagram, connected through the golden ratio φ.
Details: Calculating the short chord slice is essential for geometric constructions, architectural designs, and mathematical studies involving pentagrams and golden ratio relationships.
Tips: Enter the Long Chord Slice value in meters. The value must be positive and greater than zero for accurate calculation.
Q1: What is the golden ratio φ?
A: The golden ratio (approximately 1.618) is a mathematical constant that appears frequently in geometry, art, and nature, representing an aesthetically pleasing proportion.
Q2: How is the pentagram related to the golden ratio?
A: The pentagram contains multiple instances of the golden ratio in the relationships between its various segments and chord slices.
Q3: What are the practical applications of this calculation?
A: This calculation is used in geometric design, sacred geometry, architecture, and mathematical research involving pentagonal symmetry.
Q4: Can this formula be derived geometrically?
A: Yes, the relationship can be derived from the properties of regular pentagons and the intersecting chords theorem within pentagram constructions.
Q5: Are there other relationships between pentagram segments?
A: Yes, the pentagram contains multiple golden ratio relationships between various chord slices, diagonal lengths, and segment proportions.