Kang Seonghoon, an esoteric polyglot (sorta) programmer, avid rhythm action gamer, heavy thinker and proud preservationist. / 이 계정은 개인 계정으로 소속 회사·단체의 의견과 무관합니다.
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ALT A single square can be trivially surrounded by a convex hull of length 4. Two squares trivially take 6. Three squares can be arranged in several rows: a single row of 3 squares (8), two rows of 2 squares and 1 square where the top row is aligned to the side (6+√2 ≈ 7.414), same but where the top row is aligned to the center (5+√5 ≈ 7.236). The last is thought to be optimal, but is it?
ALT The cross-shaped arrangement of 5 squares is the best packing known in a circle, which results in a perimeter of 4+4√2 ≈ 9.656. But three rows of 2, 2 and 1 squares where the last row is centered would give a lower perimeter of 7+√5 ≈ 9.236.
ALT 441 squares can be arranged into a 21×21 grid of the perimeter 84, but also into a circular pattern where 10 squares from each corner are removed and pasted to the side of the length 13. The circular pattern has a perimeter of 40+16√2+4√13 ≈ 77.049, far shorter than the grid pattern.
ALT Talia, The most dangerous thing in an academic career, Talia, is not inadequate research, as one might think. It is antagonizing the seniors of your field, rocking the boat, stirring drama. That is not taken kindly. Many of the tenured PL professors at UIUC are friends with PL folks at Purdue. These are relationships forged over years, many of which you are likely not even aware of. People do talk. Best, anonymous R1 PL Full Professor
