1. What is Circumradius of Decagon?

The Circumradius of a Decagon is the radius of a circumcircle that touches all vertices of the decagon. It is an important geometric property used in various mathematical and engineering applications.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( R_c \) — Circumradius of Decagon (m)
• \( r_i \) — Inradius of Decagon (m)

Explanation: This formula establishes the mathematical relationship between the circumradius and inradius of a regular decagon using the golden ratio and square root functions.

3. Importance of Circumradius Calculation

Details: Calculating the circumradius is essential in geometry, architecture, and engineering for designing decagonal structures, determining spatial relationships, and solving geometric problems involving regular decagons.

4. Using the Calculator

Tips: Enter the inradius value in meters. The value must be positive and valid. The calculator will compute the corresponding circumradius using the mathematical relationship between these two properties of a regular decagon.

5. Frequently Asked Questions (FAQ)

Q1: What is a regular decagon?
A: A regular decagon is a polygon with ten equal sides and ten equal angles.

Q2: How is circumradius different from inradius?
A: Circumradius is the radius of the circle passing through all vertices, while inradius is the radius of the circle inscribed within the decagon touching all sides.

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 practical applications use this calculation?
A: This calculation is used in architectural design, mechanical engineering, and geometric modeling where decagonal shapes are involved.

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