1. What is Circumradius of Heptagon?

The circumradius of a heptagon is the radius of a circumcircle that touches all vertices of the heptagon. For a regular heptagon, this distance is constant from the center to any vertex.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_c \) — Circumradius of Heptagon (m)
• \( w \) — Width of Heptagon (m)
• \( \pi \) — Archimedes' constant (≈3.14159)
• \( \sin \) — Sine trigonometric function

Explanation: This formula calculates the circumradius based on the width of a regular heptagon using trigonometric relationships.

3. Importance of Circumradius Calculation

Details: Calculating the circumradius is important in geometry, architecture, and engineering for designing and analyzing heptagonal structures and patterns.

4. Using the Calculator

Tips: Enter the width of the heptagon in meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a regular heptagon?
A: A regular heptagon is a seven-sided polygon where all sides are equal in length and all interior angles are equal.

Q2: How is width defined for a heptagon?
A: The width of a heptagon is the horizontal distance from the leftmost edge to the rightmost edge of the regular heptagon.

Q3: What are typical applications of this calculation?
A: This calculation is used in geometric design, architectural planning, and engineering projects involving heptagonal shapes.

Q4: Can this formula be used for irregular heptagons?
A: No, this formula is specifically for regular heptagons where all sides and angles are equal.

Q5: What is the relationship between width and circumradius?
A: The width and circumradius have a fixed trigonometric relationship in a regular heptagon, as expressed in the formula.