1. What is the Circumradius of Dodecagon?

The circumradius of a dodecagon is the radius of a circumcircle that touches all twelve vertices of the regular dodecagon. It represents the distance from the center of the dodecagon to any of its vertices.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_c \) — Circumradius of Dodecagon (m)
• \( w \) — Width of Dodecagon (m)
• \( \sqrt{6}, \sqrt{2}, \sqrt{3} \) — Square roots of 6, 2, and 3 respectively

Explanation: This formula calculates the circumradius based on the width of a regular dodecagon, using mathematical constants derived from geometric properties of the shape.

3. Importance of Circumradius Calculation

Details: Calculating the circumradius is essential in geometry for determining the size and proportions of a regular dodecagon, and is used in various architectural, engineering, and design applications where twelve-sided shapes are employed.

4. Using the Calculator

Tips: Enter the width of the dodecagon in meters. The width must be a positive value greater than zero. The calculator will compute the circumradius based on the geometric relationship between width and circumradius.

5. Frequently Asked Questions (FAQ)

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 width defined for a dodecagon?
A: The width of a dodecagon is the horizontal distance from the leftmost edge to the rightmost edge of the shape.

Q3: What are typical applications of dodecagon calculations?
A: Dodecagons are used in architecture, coin design (some countries), clock faces, and various decorative patterns where twelve-fold symmetry is desired.

Q4: Can this formula be used for irregular dodecagons?
A: No, this formula applies only to regular dodecagons where all sides and angles are equal.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for regular dodecagons, with accuracy limited only by the precision of the input values and computational rounding.