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Miklós Schweitzer
1997 Miklós Schweitzer
5
5
Part of
1997 Miklós Schweitzer
Problems
(1)
area of disjoint circles in a square
Source: miklos schweitzer 1997 q5
9/27/2021
Let
a
1
>
a
2
>
a
3
>
⋯
a_1>a_2>a_3>\cdots
a
1
>
a
2
>
a
3
>
⋯
be a sequence of real numbers which converges to 0. We put circles of radius
a
1
a_1
a
1
into a unit square until no more can fit. (A previously laid circle must not be moved.) Then we put circles of radius
a
2
a_2
a
2
in the remaining space until no more can fit, continuing the process for
a
3
a_3
a
3
,... What can the area covered by the circles be?a similar problem involving circles in a square: https://artofproblemsolving.com/community/c7h1979044
geometry
real analysis