Strips in the Plane

Unknown Author February 17, 2018
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Section: Brain Teasers Category: Mathematics
Difficulty:

Prove that you can not cover the plane with infinite strips which have a total sum of their widths equal to 1.

Take a circle with radius 1 in the plane. A strip with width X covers at most an area of 2X of the circle. Therefore all strips cover at most an area of 2, which is smaller than the total area of the circle (~3.14).

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