1. What is the Circumradius of Hexadecagon?

The circumradius of a hexadecagon (16-sided polygon) is the radius of a circumcircle that touches all vertices of the hexadecagon. It represents the distance from the center of the polygon to any of its vertices.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_c \) — Circumradius of Hexadecagon
• \( d_5 \) — Diagonal across five sides of Hexadecagon
• \( \pi \) — Archimedes' constant (approximately 3.14159)
• \( \sin \) — Sine trigonometric function
• \( \sqrt{} \) — Square root function

Explanation: This formula calculates the circumradius based on the diagonal measurement across five sides, using trigonometric relationships specific to the 16-sided polygon geometry.

3. Importance of Circumradius Calculation

Details: Calculating the circumradius is essential in geometry for determining the size and proportions of regular polygons, architectural design, and various engineering applications involving polygonal shapes.

4. Using the Calculator

Tips: Enter the diagonal across five sides measurement in meters. The value must be positive and greater than zero for accurate calculation.

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 the diagonal across five sides measured?
A: The diagonal across five sides is the straight line distance between two non-adjacent vertices that have four vertices between them along the perimeter.

Q3: What are practical applications of this calculation?
A: This calculation is used in architectural design, mechanical engineering, computer graphics, and any field requiring precise geometric measurements of polygonal shapes.

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

Q5: What is the relationship between circumradius and side length?
A: For a regular hexadecagon, the circumradius can also be calculated from the side length using the formula: \( r_c = \frac{s}{2\sin(\pi/16)} \), where s is the side length.