Number of Squares That Can Fit Inside a Circle

I would like to know if there's a method on finding the largest number of squares with side lengths $x$ that can fit inside a circle with radius $y$.

Note by Kaizen Cyrus
4 months, 2 weeks ago

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I don't think there is a general method for doing this. You can calculate a rough lower bound on the number of squares of a given size that will fit inside a unit circle but it's hard to prove that you can't fit in more somehow by rearranging the squares. See https://mathworld.wolfram.com/SquarePacking.html for the first six square packings.

- 4 months, 1 week ago

Thank you for this.

- 4 months, 1 week ago