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I am trying to calculate the points around a circle with a certain distance in between each other.

Below is a graphical representation of what I am attempting to do.

The diameter is 70 (radius 35), and I want to find all the points that are 5 apart from each other.

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up vote 3 down vote accepted

Do you want the points $5$ apart around the circle, or $5$ apart on a straight line? Around the circle, you won't come out even, as the circumference is $70 \pi \approx 219.91149$. But you can come pretty close, as this is close to $220$. The angle at the center then is $\frac 5{35}=\frac 17$ radian $=\frac {180^\circ}{7\pi} \approx 8.18511^\circ$. So you can put them at $(35\cos 8.18511k^\circ,35\sin 8.18511k^\circ)$ for $k$ from $0$ to $43$. For straight lines, the central angle is $2 \arcsin \frac 1{14} \approx 8.192^\circ$ Again you don't come out even, but you can put them at $(35\cos 8.1892k^\circ,35\sin8.1892k^\circ)$ for $k$ from $0$ to $43$.

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