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The Universal Cover Problem

Imagine this for a moment: You are very skillful with the needle and thread. Your friend, who is aware of your skill, texts you, “Hey — I’ve got holes in some of my jeans. Can you patch them for me?”

You reply, “Sure, that’s easy,” and then you ask how big the holes are.

“They’re all weird shapes, but never wider than an inch. I’ll be by later, so get things ready!”

You then reach for your sewing kit and pull out some circular patches, each 1 inch in diameter. “This should do the trick,” you say to yourself. 

But will it? Can a circular patch of diameter 1 really cover any hole that is at most 1 inch wide in any direction?

You might think to yourself that this is just a simple elementary geometry problem, but this problem —called the “universal cover” problem — hasn’t been solved in 100 years.

Find out more about this over at Quanta Magazine.

(Image Credit: _Alicja_/ Pixabay)

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