rings of circles

an application of trigonometry (in right angled triangles)

a ppt is here

the task is to relate the radius of the black circles (in the ring) to the radius of the red (centre) radius

it might be simpler to put the radius of the red circle, k = 1, and find the associated value of r
or vice versus

an intention is to work towards establishing a general rule
so that e.g. if you wanted to find the relationship between the radii for a 50 circle ring you could do so with a formula

surds can be involved for some of the cases

what relationships are there between the radii of the three different sized circles?

prove that r = k

two of Damien Hirst's pictures