What is the area covered by these circles? (Try 2 -- I hit Post when I meant Edit)
This problem's question is: What is the area covered by these circles?
Starting with three unit disks, mutally tangent, within the space between the disks that are already present, add smaller disks tangent to the three disks surrounding the open space, continuing adding disks tangent to the disks surrounding open spaces ad infinitum. The answer was added as a real number approximation with three places to the right of the decimal point. The area includes the original three unit disks.
The answer is 9.586.
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1 solution
Area ⎣ ⎡ RegionUnion ⎣ ⎡ ⎩ ⎨ ⎧ Disk [ { 0 , 0 } , 1 ] , Disk [ { 2 , 0 } , 1 ] , Disk [ { 1 , 3 } , 1 ] , Triangle ⎣ ⎡ ⎝ ⎛ 0 2 1 0 0 3 ⎠ ⎞ ⎦ ⎤ ⎭ ⎬ ⎫ ⎦ ⎤ ⎦ ⎤ ⇒ 2 1 ( 2 3 + 5 π ) ≈ 9 . 5 8 6 0 3 2 4 4 1 5 4 3 3 6
Note: that that is the area of two and one-half unit disk areas plus the area of the equilateral triangle.