Short Diagonal of Heptagon given Inradius Calculator

Short Diagonal Formula:

\[ d_{Short} = 4 \times r_i \times \tan\left(\frac{\pi}{7}\right) \times \cos\left(\frac{\pi}{7}\right) \]

Short Diagonal of Heptagon: m

1. What is Short Diagonal of Heptagon given Inradius?

Definition: This calculator computes the length of the short diagonal of a regular heptagon based on its inradius (radius of inscribed circle).

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

2. How Does the Calculator Work?

The calculator uses the formula:

\[ d_{Short} = 4 \times r_i \times \tan\left(\frac{\pi}{7}\right) \times \cos\left(\frac{\pi}{7}\right) \]

Where:

\( d_{Short} \) — Short diagonal of heptagon (meters)
\( r_i \) — Inradius of heptagon (meters)
\( \pi \) — Mathematical constant (~3.14159)
\( \tan \) — Tangent trigonometric function
\( \cos \) — Cosine trigonometric function

Explanation: The formula relates the inradius to the short diagonal through trigonometric functions of π/7 (the central angle of a heptagon).

3. Importance of Short Diagonal Calculation

Details: Knowing the short diagonal helps in determining heptagon proportions, designing heptagonal structures, and solving geometric problems.

4. Using the Calculator

Tips: Enter the inradius in meters and optional tolerance percentage (±5%). The result shows the short diagonal length.

5. Frequently Asked Questions (FAQ)

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

Q2: What's the difference between short and long diagonals?
A: Short diagonal connects vertices two apart, long diagonal connects three apart in a heptagon.

Q3: Why is π/7 used in the formula?
A: It represents half the central angle (360°/14) of a heptagon.

Q4: When would I use the tolerance field?
A: To account for manufacturing tolerances or material expansion/contraction.

Q5: Can I use this for irregular heptagons?
A: No, this calculator only works for regular (symmetrical) heptagons.