1. What is the Chord Length of Star Pyramid?

The Chord Length of Star Pyramid is the length of the straight line joining two adjacent spike points or outer vertices of the base of the Star Pyramid. It represents the distance between two consecutive points of the star-shaped base.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( l_c \) — Chord Length of Star Pyramid (m)
• \( \phi \) — Golden ratio (≈1.618034)
• \( l_{e(Pentagon)} \) — Pentagonal Edge Length of Base of Star Pyramid (m)

Explanation: The formula calculates the chord length by multiplying the square of the golden ratio with the pentagonal edge length of the base.

3. Importance of Chord Length Calculation

Details: Calculating the chord length is essential for understanding the geometric properties of star pyramids, determining proportions, and ensuring accurate construction of star pyramid models.

4. Using the Calculator

Tips: Enter the pentagonal edge length of the base in meters. The value must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is the golden ratio (φ)?
A: The golden ratio is a mathematical constant approximately equal to 1.618034, often found in geometry, art, and nature.

Q2: How is the chord length related to the pentagonal edge length?
A: The chord length is directly proportional to the pentagonal edge length, scaled by the square of the golden ratio.

Q3: Can this formula be used for any star pyramid?
A: This specific formula applies to star pyramids with a pentagrammic base constructed from a regular pentagon.

Q4: What are typical values for pentagonal edge length?
A: The pentagonal edge length can vary depending on the specific application, but it's typically measured in meters or appropriate length units.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact when using the precise value of the golden ratio, though practical measurements may introduce some error.