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The circumradius of a dodecagon is the radius of a circumcircle that touches all twelve vertices of the dodecagon. It represents the distance from the center of the dodecagon to any of its vertices.
The calculator uses the formula:
Where:
Explanation: This formula establishes a direct relationship between the diagonal spanning three sides of a regular dodecagon and its circumradius through a simple division by the square root of 2.
Details: Calculating the circumradius is essential in geometry for determining the size and proportions of a dodecagon, particularly in architectural design, engineering applications, and mathematical modeling of twelve-sided polygons.
Tips: Enter the diagonal across three sides of the dodecagon in meters. The value must be positive and greater than zero for accurate calculation.
Q1: What is a regular dodecagon?
A: A regular dodecagon is a twelve-sided polygon where all sides are equal in length and all interior angles are equal (150 degrees each).
Q2: How is the diagonal across three sides measured?
A: The diagonal across three sides connects two non-adjacent vertices with exactly two vertices between them along the perimeter of the dodecagon.
Q3: Can this formula be used for irregular dodecagons?
A: No, this specific formula applies only to regular dodecagons where all sides and angles are equal.
Q4: What are practical applications of dodecagon calculations?
A: Dodecagons are used in architecture (building designs), engineering (bolt patterns), and various decorative and structural applications where twelve-fold symmetry is desired.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact for regular dodecagons, with accuracy depending on the precision of the input measurement.