1. What is the Circumradius of Hexadecagon?

The circumradius of a hexadecagon is the radius of a circumcircle touching each of the hexadecagon's vertices. A hexadecagon is a polygon with 16 sides and 16 angles.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_c \) — Circumradius of Hexadecagon (m)
• \( h \) — Height of Hexadecagon (m)
• \( \pi \) — Archimedes' constant (approximately 3.14159)
• \( \sin \) — Sine trigonometric function
• \( \sqrt{} \) — Square root function

Explanation: This formula calculates the circumradius based on the height of the hexadecagon, using trigonometric relationships and square root operations.

3. Importance of Circumradius Calculation

Details: Calculating the circumradius is important in geometry for determining the size of the circumscribed circle around a hexadecagon, which has applications in various fields including architecture, engineering, and design.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is a hexadecagon?
A: A hexadecagon is a polygon with 16 sides and 16 angles. It is also known as a 16-gon.

Q2: How is circumradius different from inradius?
A: Circumradius is the radius of the circumscribed circle (touching all vertices), while inradius is the radius of the inscribed circle (touching all sides).

Q3: Can this formula be used for other polygons?
A: No, this specific formula is designed for hexadecagons. Other polygons have different formulas for calculating circumradius.

Q4: What are the practical applications of this calculation?
A: This calculation is useful in architectural design, mechanical engineering, and geometric modeling where hexadecagonal shapes are used.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise when using the exact formula, though computational precision may vary slightly depending on the implementation.