Inspired by toilet paper

Geometry Level 3

Referring to the figure above, suppose A1A_1 is area of first white circle, then A2A_2 is area of pink annulus, A3A_3 is area of blue annulus and like wise AnA_n would be the annulus bounded by nthn^\text{th} and (n1)th(n-1)^\text{th} circle. These nn concentric circles are drawn such that the area bounded by two concentric circles remains constant, that is A1=A2=A3==AnA_1=A_2=A_3= \cdots = A_n.

Define rnr_n to be the radius of nthn^\text{th} circle.Evaluate r100r1\dfrac{r_{100}}{r_1} correct 2 decimal places.


Inspiration.

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