7
votes
2answers
236 views

Chances of avoiding the diagonal

A circle of radius 1 is randomly placed in a rectangle $ABCD$ so that the circle lies completely inside the rectangle. Length and breadth of rectangles are 36 and 15 respectively. Let the ...
0
votes
1answer
79 views

How to find out the probability of ordered pairs of rational or irrational number $(a,b)$ such that $1<a<50, 1,<b<50$, and $\log_b a$ is rational.

How to find out the probability of ordered pairs of rational or irrational or transcendental number $(a,b)$ such that $1<a<50$, $1<b<50$, and $\log_b a$ is rational? Uniformly ...
5
votes
1answer
170 views

Is this graph based on rationals familiar?

Has anyone come across a graph like this? The black circles represent rationals in $(0,1)$ and their heights are roughly proportional to the reciprocal of the square of their lowest terms ...