30 dots equally spaced within a 20” diameter circle, what is the distance between each dot

Question

I have a 20” disk that requires 30 ball bearings to be equally spaced between each other on the disk. What would be the equal distance from each other within that 20” disk?

Answer 1

 

 

The pictures show a uniform configuration of dots in the circle of radius 10 inches.

The lower picture is a magnification of part of the upper figure.

Angle POA is arctan(AP/PO)=½a/3a=⅙. So sinPOA=1/√37 (using Pythagoras).

AP=AOsinPOA=10/√37 because AO=10, radius of the circle. So a/2=10/√37, and a=3.288" approx.

The lattice has a spacing of 3.288".

There are other configurations of 30 dots, for example, where 3 dots form the vertices of an equilateral triangle. The picture below shows a combination of squares and equilateral triangles.

The red dot and line show the centre and radius of the circle.