Circumradius of Heptagon given Long Diagonal Calculator

Circumradius Formula:

\[ r_c = \frac{d_{Long} \times \sin\left(\frac{\pi/2}{7}\right)}{\sin\left(\frac{\pi}{7}\right)} \]

Circumradius: %

1. What is Circumradius of Heptagon?

Definition: The circumradius of a heptagon is the radius of the circumscribed circle that passes through all vertices of the heptagon.

Purpose: It helps in geometric calculations and design of heptagonal shapes in architecture and engineering.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_c = \frac{d_{Long} \times \sin\left(\frac{\pi/2}{7}\right)}{\sin\left(\frac{\pi}{7}\right)} \]

Where:

\( r_c \) — Circumradius of heptagon (%)
\( d_{Long} \) — Long diagonal of heptagon (%)

Explanation: The formula relates the long diagonal of a regular heptagon to its circumradius using trigonometric functions of angles based on π/7.

3. Importance of Circumradius Calculation

Details: Knowing the circumradius is essential for constructing precise heptagonal shapes and for various geometric computations.

4. Using the Calculator

Tips: Enter the long diagonal measurement in percentage (with ±5% tolerance). The result will be the circumradius in percentage.

5. Frequently Asked Questions (FAQ)

Q1: What is a regular heptagon?
A: A regular heptagon is a seven-sided polygon with all sides and angles equal.

Q2: Why use trigonometric functions in this calculation?
A: The angles in a heptagon are based on π/7 radians, making trigonometric functions essential for these calculations.

Q3: What does the ±5% mean?
A: This indicates the acceptable tolerance range for the input value.

Q4: Can I use this for irregular heptagons?
A: No, this calculator is specifically for regular heptagons where all sides and angles are equal.

Q5: How precise is this calculation?
A: The calculation is mathematically precise for regular heptagons, though real-world measurements may have slight variations.