- pi !
Find the value of: f( ) - f( )
The function f(r) is defined to give out the fraction of area covered by the path traced by a point on a circle of radius r filled between the circle of radius (r+1) and the circle of radius 1.
rotating around a circle of radius 1.
Note:- The width of the path is infinitely small and the circle revolves for an infinite time.
see this graph
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We see that any circle with a rational number as radius will retrace itself after finite amount of time so will draw a path of finite length hence zero
area will be covered however a circle with irrational number will never retrace itself so will make an infinitely long path and will cover the whole area
so will give 1. hence the answer is 1-0=1