Math problems are Mohr fun when they involve circles.

Given `0 < t`

and _{x} < R_{x}`0 < t`

, two concentric but not necessarily similar ellipses are defined as _{y} < R_{y}`x`

and ^{2}/R_{x}^{2} + y^{2}/R_{y}^{2} = 1`x`

.
^{2}/(R_{x} - t_{x})^{2} + y^{2}/(R_{y} - t_{y})^{2} = 1

Two circles, C_{1} and C_{N} are defined as `(x - R`

and _{x} + t_{x}/2)^{2} + y^{2} = (t_{x}/2)^{2}`(y - R`

.
_{y} + t_{y}/2)^{2} + x^{2} = (t_{y}/2)^{2}

In between these circles are `(N-2)`

circles denoted C_{2} through C_{N-1} with respective radii r_{2} through r_{N-1} whose edges are tangent to both ellipses and whose maximum overlap with each adjacent circle is given by

where `m`/2 × (r_{n} + r_{n+1})`0 ≤ `

, r`m` < 1_{n} is the radius of one circle and r_{n+1} is the radius of the adjacent circle.

Find the number of circles N, the minimum possible constant value of the overlap ratio `m`, and the center coordinates and radii of all the circles.

Alternate problem: Instead of starting with C_{1} and C_{N} defined as circles centered on the axes, C_{1} and C_{N} are tangent to both ellipses and overlap the x and y axes, respectively, by

and `m`r_{1}

, respectively.
`m`r_{N}

Why do we care? By drawing every other circle, we can create a dotted CSS borders for curved corners. :)