If you’re wondering whether you get the same donut fix with a square donut as you would with a round one, this site is nothing if not proleptic, and has antipated your concern. The math has been done. But it’s just gibberish to us:
“A round donut with radius R1 occupies the same space as a square donut with side 2R1. If the center circle of a round donut has a radius R2 and the hole of a square donut has a side 2R2, then the area of a round donut is πR12 – πr22. The area of a square donut would be then 4R12 – 4R22. This doesn’t say much, but in general and throwing numbers, a full box of square donuts has more donut per donut than a full box of round donuts.
“The interesting thing is knowing exactly how much more donut per donut we have. Assuming first a small center hole (R2 = R1/4) and replacing in the proper expressions, we have a 27,6% more donut in the square one (Round: 15πR12/16 ≃ 2,94R12, square: 15R12/4 = 3,75R12). Now, assuming a large center hole (R2 = 3R1/4) we have a 27,7% more donut in the square one (Round: 7πR12/16 ≃ 1,37R12, square: 7R12/4 = 1,75R12). This tells us that, approximately, we’ll have a 27% bigger donut if it’s square than if it’s round.”