1. What is Circumradius of Nonagon?

The Circumradius of Nonagon is the radius of a circumcircle touching each of the vertices of the Nonagon. 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 Nonagon (m)
• \( h \) — Height of Nonagon (m)
• \( \pi \) — Archimedes' constant (≈ 3.14159)
• \( \cos \) — Cosine trigonometric function

Explanation: This formula calculates the circumradius of a regular nonagon based on its height, using the mathematical relationship between these geometric properties.

3. Importance of Circumradius Calculation

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

4. Using the Calculator

Tips: Enter the height of the nonagon in meters. The value must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is a regular nonagon?
A: A regular nonagon is a nine-sided polygon with all sides equal and all interior angles equal (140° each).

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 polygon touching all sides.

Q3: Can this formula be used for irregular nonagons?
A: No, this formula applies only to regular nonagons where all sides and angles are equal.

Q4: What are practical applications of nonagon geometry?
A: Nonagonal shapes are used in architecture, design, coins (some countries), and various decorative patterns.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for regular nonagons, limited only by the precision of the input values and computational floating-point accuracy.