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My idea would be to optimise the spacing of the stars by using circle packing algorithms. Find the largest radius for which you can fit 51 circles in the rectan
by OscarCunningham 6y ago
My idea would be to optimise the spacing of the stars by using circle packing algorithms. Find the largest radius for which you can fit 51 circles in the rectangle, and then center the stars in the circles. That guarantees that the stars are well spaced.
- pietor 6y agoPacking doesn’t necessarily make nice symmetrical things. I don’t have an image for n=51 but this [1] is for 55. Interestingly for square numbers from 49 on, the best packing is not the obvious square lattice either [2] [1]: https://www.ime.usp.br/~egbirgin/packing/packing_by_nlp/numerical.php?table=csq-mina&title=Packing%20of%20unitary-radius%20circles%20in%20a%20square https://www.ime.usp.br/~egbirgin/packing/packing_by_nlp/nume... [2]: https://www.ime.usp.br/~egbirgin/packing/packing_by_nlp/numerical.php?table=csq-mina&title=Packing%20of%20unitary-radius%20circles%20in%20a%20square https://www.ime.usp.br/~egbirgin/packing/packing_by_nlp/nume...