# 3D Math - How accurate should a circle be?

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If you want to draw an accurate circle using straight lines - how many do you need?

Assuming you'd like your line to lie within one pixel of the true edge, then the largest radius you can draw with an N-sided polygon is:

``` R = 1 / (1 - cos ( PI / numSides ))
```

3 sides 2 radius 4 sides 3 radius 5 sides 5 radius 6 sides 7 radius 7 sides 10 radius 8 sides 13 radius 9 sides 17 radius 10 sides 20 radius 11 sides 25 radius 12 sides 29 radius 13 sides 34 radius 14 sides 40 radius 15 sides 46 radius 16 sides 52 radius 17 sides 59 radius 18 sides 66 radius 19 sides 73 radius 20 sides 81 radius 21 sides 90 radius 22 sides 98 radius 23 sides 107 radius 24 sides 117 radius 25 sides 127 radius 26 sides 137 radius 27 sides 148 radius 28 sides 159 radius 29 sides 171 radius 30 sides 183 radius 31 sides 195 radius 32 sides 208 radius 33 sides 221 radius 34 sides 234 radius 35 sides 248 radius 36 sides 263 radius 37 sides 278 radius 38 sides 293 radius 39 sides 308 radius 40 sides 324 radius 50 sides 507 radius 60 sides 730 radius 70 sides 993 radius 80 sides 1300 radius 90 sides 1600 radius 100 sides 2000 radius 120 sides 2900 radius 140 sides 4000 radius 160 sides 5200 radius 180 sides 6600 radius 200 sides 8100 radius 220 sides 9800 radius 240 sides 11700 radius 255 sides 13200 radius