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The Distance of Tips of Concave Regular Pentagon is the length of the line joining the two upper tips of the Concave Regular Pentagon. It represents a key geometric measurement in this specific pentagon configuration.
The calculator uses the formula:
Where:
Explanation: This formula establishes a direct proportional relationship between the perimeter of the concave regular pentagon and the distance between its upper tips, using the golden ratio constant.
Details: Calculating the distance between tips is essential for geometric analysis, architectural design, and pattern creation involving concave regular pentagons. It helps in determining the overall dimensions and proportions of the shape.
Tips: Enter the perimeter of the concave regular pentagon in meters. The value must be positive and greater than zero for accurate calculation.
Q1: What is a concave regular pentagon?
A: A concave regular pentagon is a five-sided polygon with equal side lengths but with at least one interior angle greater than 180 degrees, creating an indented shape.
Q2: Why does the formula include the square root of 5?
A: The square root of 5 appears due to the mathematical relationship with the golden ratio (φ), which is fundamental in pentagonal geometry.
Q3: Can this formula be used for convex regular pentagons?
A: No, this specific formula applies only to concave regular pentagons. Convex regular pentagons have different geometric properties and relationships.
Q4: What are practical applications of this calculation?
A: This calculation is used in geometric design, architectural patterns, artistic compositions, and mathematical studies of pentagonal shapes.
Q5: How accurate is this formula?
A: The formula is mathematically exact for perfect concave regular pentagons and provides precise results when accurate perimeter measurements are provided.