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The formula calculates the side length of a regular decagon when the diagonal across five sides is known. This geometric relationship is derived from the properties of regular polygons and the golden ratio.
The calculator uses the formula:
Where:
Explanation: The formula utilizes the mathematical relationship between the diagonal spanning five sides and the side length in a regular decagon, incorporating the golden ratio constant.
Details: Calculating the side length of a decagon is essential in geometry, architecture, and design applications where regular decagonal shapes are used. It helps in determining dimensions and proportions accurately.
Tips: Enter the diagonal across five sides in meters. The value must be positive and greater than zero for valid calculation.
Q1: What is a regular decagon?
A: A regular decagon is a polygon with ten equal sides and ten equal angles.
Q2: Why does the formula include √5?
A: The square root of 5 appears due to the golden ratio relationship inherent in the geometry of regular decagons.
Q3: Can this formula be used for irregular decagons?
A: No, this formula applies only to regular decagons where all sides and angles are equal.
Q4: What are practical applications of this calculation?
A: This calculation is useful in architectural design, engineering projects, and mathematical studies involving regular polygons.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact for regular decagons, though practical measurements may have slight variations.