Donuts make it BETTER

I think a couple of weeks ago I found this photo just surfing the internet:

dococtillery: lthmath: This thing made my day ;) Enjoy 😀 Actually, using their (incorrect) method, the ratio will always be 4/pi, thus no matter the ratio of the hole to the total, the square is 27% bigger.Its incorrect however, because this assumes the donuts are flat. If we treat them in 3D (much tastier that way) with height (R1-R2), then the volume of a Torus with the defined R1 and R2 as above, is V1= pi^2*(R1-R2)^2(R2+R1)/4. For the square, we simply need to extrude the area given above to make it 3D,and assuming it is actually square in crossection, we have V2 = 4(R1^2-R2^2)*(R1-R2) = 4(R1-R2)^2(R1+R2).Thus the ratio of the square to the circular donuts is: RATIO  = V2/V1 = 16/pi^2, which is approximately 1.62. Thus the square donut is actually 62% bigger than the circle donut. Fun note, the ratio of the 2D donuts is 4/pi. by adding another dimension, we squared the ratio. TL;DR: Square donut is actually 62% bigger. Though I don’t agree that the method in the photo is incorrect (it is just a 2D solution for the problem, maybe we can say they omitted the height 😉), but I have to agree that the 3D (more realistic method) is awesome 😊 now we have the complete proof… 😉We should totally make square donuts from now on 🍩😊

“I thought it is an incredibly fun explanation for why square donuts feet better in the box, and also we get extra product, too. The thing with the explanation in the photo is that it is perfect for the 2D case, and not the real (3D) model we eat and see in the shops. But I still think it is incredible, so I decided to post it on Tumblr, and this is what happened:

  • If we treat them in 3D (much tastier that way) with height (R1-R2), then the volume of a Torus with the defined R1 and R2 as above, is V1= pi^2*(R1-R2)^2(R2+R1)/4. For the square, we simply need to extrude the area given above to make it 3D,and assuming it is actually square in crossection, we have V2 = 4(R1^2-R2^2)*(R1-R2) = 4(R1-R2)^2(R1+R2). Thus the ratio of the square to the circular donuts is: RATIO  = V2/V1 = 16/pi^2, which is approximately 1.62. Thus the square donut is actually 62% bigger than the circle donut.Fun note, the ratio of the 2D donuts is 4/pi. by adding another dimension, we squared the ratio.TL;DR: Square donut is actually 62% bigger.” by I Like Puns

  • “See? Maths is everywhere” by Because Why Not 

  • “Tumblr: where people take math related to real life and the shape of donuts seriously” by that girl

  • “That’s only the two-dimensional case. I just worked out the three-dimensional case with certain assumptions. The result: rectangular donuts have 62% more donut per donut.” by A really hoopy frood.image

  • “This is the best post I ever expect to come by. Donut examples will forever be that much better.” by Untitled and Unbridled

  • “Hahahaha, una dona cuadrada tiene un cuarto más de dona por dona que una dona redonda. QUIÉN LO DIRÍA!!”  by . (dot)

I thought it would be fun to share with you all the enthusiasm people have when it comes to donuts, even mathematics becomes fun and important. I would like to say thank you to everyone that found time to think about this and consider the 3D ( more realistic ) problem. So lets start and make square donuts!! ^_^

Hope you had a great day. Thank you for reading and enjoy your week. You can find me on Facebook,  Tumblr,  Google+,   Twitter  and  Instagram. Don’t forget that maths is everywhere and eat your donuts ^_^

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2 thoughts on “Donuts make it BETTER

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  1. The 2 dimensional analysis is still useful as an approximation of how much extra chocolate frosting you get if you choose that version. Of course, purists will not be satisfied with that, and neither should you. So, challenge for the extra eager students: what is the area covered by chocolate frosting on top of a toroidal donut?

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