Circumradius Of N Gon Calculator

Circumradius of N-gon Formula:

\[ r_c = \frac{l_e}{2 \times \sin(\pi / N_{\text{Sides}})} \]

Circumradius of N-gon:

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1. What is the Circumradius of N-gon?

The circumradius of an N-gon (regular polygon) is the radius of the circumscribed circle that passes through all the vertices of the polygon. It represents the distance from the center of the polygon to any of its vertices.

2. How Does the Calculator Work?

The calculator uses the circumradius formula:

\[ r_c = \frac{l_e}{2 \times \sin(\pi / N_{\text{Sides}})} \]

Where:

\( r_c \) — Circumradius of N-gon (m)
\( l_e \) — Edge Length of N-gon (m)
\( N_{\text{Sides}} \) — Number of Sides of N-gon
\( \pi \) — Archimedes' constant (approximately 3.14159)
\( \sin \) — Sine trigonometric function

Explanation: The formula calculates the circumradius based on the edge length and number of sides using trigonometric relationships in a regular polygon.

3. Importance of Circumradius Calculation

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

4. Using the Calculator

Tips: Enter the edge length in meters and the number of sides (must be at least 3). All values must be valid positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a regular polygon?
A: A regular polygon is a geometric figure with all sides equal in length and all angles equal in measure.

Q2: Can this calculator be used for irregular polygons?
A: No, this calculator is specifically designed for regular polygons where all sides and angles are equal.

Q3: What's the minimum number of sides required?
A: The minimum number of sides is 3, which corresponds to an equilateral triangle.

Q4: How does the circumradius relate to the inradius?
A: The circumradius is always equal to or larger than the inradius (radius of the inscribed circle) for any regular polygon.

Q5: What are some practical applications of this calculation?
A: This calculation is used in architecture for designing polygonal structures, in engineering for mechanical parts, and in computer graphics for rendering regular shapes.