Equation for spacing of elements on the edge of a circle I'm trying to come up with an equation which, given an index within an arbitary number of elements (the most natural example would be 12, as in 12 numbers on a clock), along with an arbitrary radius, provides the point at which that element should be placed.
For example, if we are to use the example of a clock, and consider the center of the circle as the point [0, 0], and using a radius of, say, 100, then the '12' would be located at [0, -100], the '3' located at [100, 0], the '6' at [0, -100], and so on.
Does anyone know of an equation I could use to find the point for an arbitrary index using an arbitrary number of elements?
Thanks!
 A: and welcome to the site.
Suppose you have $n$ elements, and you want to look at the co-ordinates of the $i$th element, and you have a radius of $r$.  Then the co-ordinates are simply:
$(r\cdot\cos(2\pi\cdot\frac{i}{n}),r\cdot\sin(2\pi\cdot\frac{i}{n}))$
Or if you're more used to using degrees than radians:
$(r\cdot\cos(360^\circ\cdot\frac{i}{n}),r\cdot\sin(360^\circ\cdot\frac{i}{n}))$
This assumes that your circle is centered at $(0,0)$.  If your circle is centered instead at $(a,b)$, then you simply add $a$ and $b$ to your co-ordinates:
$(a + r\cdot\cos(2\pi\cdot\frac{i}{n}),b + r\cdot\sin(2\pi\cdot\frac{i}{n}))$
In these cases, per common mathematical convention, the numbering starts along the $x$-axis with $i=1$, and goes around evenly until $i=n-1$.  If $i=n$ it simply starts again.  If you need to change the direction or starting point, that is also possible.
For example, if you wanted to start at $90^\circ$, simply add $90^\circ$ inside the trig function (or $\pi/2$ if you're working with radians):
$(a+r\cdot\cos(360^\circ\cdot\frac{i}{n}+90^\circ),r\cdot\sin(360^\circ\cdot\frac{i}{n}+90^\circ))$
