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 is an important geometric property used in various mathematical and engineering applications.

2. How Does the Calculator Work?

The calculator uses the circumradius formula:

Where:

• \( r_c \) — Circumradius of Dodecagon (m)
• \( S \) — Side of Dodecagon (m)
• \( \sqrt{6} \) — Square root of 6
• \( \sqrt{2} \) — Square root of 2

Explanation: The formula calculates the circumradius based on the side length of a regular dodecagon using specific mathematical constants derived from geometric properties.

3. Importance of Circumradius Calculation

Details: Calculating the circumradius is essential for geometric design, architectural planning, and various engineering applications where precise measurements of regular polygons are required.

4. Using the Calculator

Tips: Enter the side length of the dodecagon in meters. The value must be positive and valid for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a dodecagon?
A: A dodecagon is a twelve-sided polygon with equal sides and equal angles in a regular dodecagon.

Q2: How is circumradius different from inradius?
A: Circumradius is the radius of the circle that passes through all vertices, while inradius is the radius of the circle inscribed within the polygon.

Q3: Can this formula be used for irregular dodecagons?
A: No, this formula is specifically for regular dodecagons where all sides and angles are equal.

Q4: What are practical applications of this calculation?
A: This calculation is used in architectural design, mechanical engineering, and geometric pattern creation.

Q5: How accurate is this formula?
A: The formula is mathematically exact for regular dodecagons and provides precise results when correct inputs are provided.