I’ve been dating this guy named tom for 4 weeks now and last night we were going on a date and he wouldn’t tell me what we were doing or where we were going.
So when I got to his we made pancakes because he didn’t get to celebrate pancake day and it was very messy but I mastered the pancake flip after a bit of tuition… Then we headed into manchester and he took me to cloud 23 in the Hilton hotel where we had cocktails and the view was just fantastic like just wow. Then I thought that would be it but we then went to one of those bars that has a bowling alley in it and had more drinks and played bowling really badly as we were so drunk. Then when we got home we ordered a dominoes and he went to pick it up and when I opened it he left this message inside x).
I couldn’t help but take photos because it was so cute and no-one has ever treated me so nice I am not worthy of this lovely lovely human being.
and he said yes (he missed that bit out)
… Y’see, now, y’see, I’m looking at this, thinking, squares fit together better than circles, so, say, if you wanted a box of donuts, a full box, you could probably fit more square donuts in than circle donuts if the circumference of the circle touched the each of the corners of the square donut.
So you might end up with more donuts.
But then I also think… Does the square or round donut have a greater donut volume? Is the number of donuts better than the entire donut mass as a whole?
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.
tl;dr: Square donuts have a 27% more donut per donut in the same space as a round one.
Thank you donut side of Tumblr.
This is the highest and best use of conic sections I have ever seen.