The formula to calculate the circumradius of a regular polygon is:
\[ r_c = \frac{l_e}{2 \sin\left(\frac{\pi}{N_S}\right)} \]
Where:
The circumradius of a regular polygon is the radius of a circumcircle touching each of the polygon's vertices.
The edge length of a regular polygon is the length of one of its sides.
The number of sides of a regular polygon denotes the total number of sides of the polygon.
Let's assume the following values:
Using the formula:
\[ r_c = \frac{10}{2 \sin\left(\frac{\pi}{8}\right)} \approx 13.0656296487638 \, \text{meters} \]
The circumradius of the regular polygon is approximately 13.0656296487638 meters.
| Edge Length (m) | Number of Sides | Circumradius (m) |
|---|---|---|
| 5 | 3 | 2.886751345948 |
| 5 | 4 | 3.535533905933 |
| 5 | 5 | 4.253254041760 |
| 5 | 6 | 5.000000000000 |
| 5 | 7 | 5.761912177406 |
| 5 | 8 | 6.532814824382 |
| 5 | 9 | 7.309511000408 |
| 5 | 10 | 8.090169943749 |
| 10 | 3 | 5.773502691896 |
| 10 | 4 | 7.071067811865 |
| 10 | 5 | 8.506508083520 |
| 10 | 6 | 10.000000000000 |
| 10 | 7 | 11.523824354812 |
| 10 | 8 | 13.065629648764 |
| 10 | 9 | 14.619022000815 |
| 10 | 10 | 16.180339887499 |
| 15 | 3 | 8.660254037844 |
| 15 | 4 | 10.606601717798 |
| 15 | 5 | 12.759762125281 |
| 15 | 6 | 15.000000000000 |
| 15 | 7 | 17.285736532219 |
| 15 | 8 | 19.598444473146 |
| 15 | 9 | 21.928533001223 |
| 15 | 10 | 24.270509831248 |