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Chord Length of Pentagram Formula:
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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.
The calculator uses the formula:
Where:
Explanation: The chord length of a pentagram is directly proportional to the edge length of the underlying pentagon, with the golden ratio as the constant of proportionality.
Details: Calculating the chord length is essential in geometric design, architecture, and artistic applications involving pentagrams. It helps in understanding the mathematical relationships and proportions within this sacred geometric shape.
Tips: Enter the pentagonal edge length 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 is a mathematical constant approximately equal to 1.6180339887. It appears frequently in geometry, art, architecture, and nature.
Q2: Why is the golden ratio used in pentagram calculations?
A: The golden ratio is intrinsically related to pentagrams and pentagons. The ratio between the chord length and the edge length of the pentagon equals the golden ratio.
Q3: Can this calculator be used for any pentagon size?
A: Yes, the formula applies to all regular pentagons regardless of size, as long as the pentagon is regular (all sides and angles equal).
Q4: What are some practical applications of pentagram geometry?
A: Pentagram geometry is used in architectural design, artistic compositions, religious symbolism, and various decorative patterns.
Q5: How accurate is the golden ratio value used in this calculator?
A: The calculator uses the golden ratio with high precision (approximately 1.6180339887498948482) to ensure accurate results.