My box of doughnut holes cereal is leaving a terrible taste in my mouth! I’m many years removed from even basic geometry but isn’t a torus a far better glaze delivery solid than a sphere? Wouldn’t a sphere have the absolute least surface area of any cereal shape? And I can’t understand why a formula for a three dimensional object would only be 2. Is this just nonsense? Help my remedial ass understand!
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It is utter nonsense. In fact, a sphere is the worst possible shape to deliver more glaze.
A sphere is the shape with the lowest possible ratio of surface area to volume. Meaning that given a specific amount of dough, and having the shape covered with a specific thickness of glaze, you actually couldn't have less glaze than if you have a sphere.
But hear me out. If you flatten the sphere, and use tomato sauce as a glaze, covered with an insulation layer of grated mozzarella, and the baked the flattened sphere until the cheese is golden brown, would it still be the worst possible shape?
My apologies - it's lunch time and I'm waiting in a lab for blood tests. At this point, everything revolves around food.
No apology necessary. The flattened sphere of food is worthy to join Trains and Crabs when it comes to universally convergent outcomes.
What if it was more of a cylinder? How would you remove the glaze without damaging the cylinder?
You would not, as the cylinder is inherently self glazing.
u/Smart_Calendar1874 may know the answer
u/Smart_Calender1874
Still holding
My eyes have glazed over from waiting.
Good, because it is imperative that the cylinder remain unharmed!
Well here we are again, 🎶
It is imperative the glaze is removed from the cylinder..
It should be fairly easy, so long as the cylinder is not attached to a larger structure.
Hol up, everything becomes a train? Cliff notes or a link to something not written by my class mates who never made it past grade school would be appreciated
there's a joke about how engineers keep coming up with ways to improve cars/busses/etc. that would actually just turn them into trains (because trains are a way more efficient means of transport)
The most common convergent food is when you fold your flattened sphere in half and pinch the edges together, keeping the toppings on the inside.
Your dumpling/ravioli/pierogi/pasty/knish/bao/samosa/calzone/borek/empanada is now ready to eat.
Mochi*
No topology necessary. The flattened sphere of food is worthy to join Convex Trains and Simply Connected Crabs when it comes to universally convergent outcomes.
Probably hard for me to fully grasp without understanding the underlying math (I don’t have enough physics background to understand the interplay of tomato sauce here) but I’ve been thinking, the perfect shape is the flattest. Imagine a cereal piece, nearly two dimensional, to maximize surface area, then increase it further with peaks and valleys. I call this theoretical shape a “flake.”
If I could figure out how to frost said flake with glaze, I think I might actually have found the perfect glazed cereal shape.
Frosted Flakes is gaslighting everyone to save % on glaze, the shrinkflation is real.
flat is good, but the best is a really long, thin, shape, as theres more dimensions to cover with glaze, basically a noodle
Ah, but storage of that noodle will prove difficult. Going with a simple solid with an infinite coastline, we can get infinite glaze on a finite amount of dough in a finite container. So long as the glaze has no thickness itself.
The flattened sphere has more surface area but you're probably only utilizing half the surface area and leaving the bottom half plain.
Hey r/ISS what are your thoughts on double sided pizza? Should we mere gravity well dwellers be jealous?
Following
I mean, it's better than a sphere is what I'm hearing, but I'm not sure where you're going with all these redlines to the assembly instructions. What weird ingredients you gonna add on your doughnut hole next? Sausage?
Pineapple
Perhaps a type of fungi, thinly sliced, and an overabundance of thinly sliced sausage.
If my grandmother had wheels she’d be a bicycle.
Flat, just like the Earf
you’re not getting it, imagine if your chicken parmesan was a flattened torus with a crispy edge not just on the outside, but in the center as well, with that central hole being filled with sauce and cheese
Don't forget to add slices of smaller sized spheres (made of meat).
Peanutbutter pickle sandwich.
That would be a pizza, silly!
Sounds like a grilled cheese to me.
A flat disc is also one of the better shapes if you want to maximize surface area, but don't want to deal with math, so you might be onto something.
you made one fatal mistake. You assumed a constant volume of a single sphere. Its reasonable to compare volume of material being glazed to equal volume in other shapes, but they are being done in different quantities. 2 small spheres have more surface area per volume than one big sphere, so many tiny sphere is far from the worst surface area to volume ratio. Now tiny donuts where each one matched the volume of the tiny spheres would be better still, but do we have the manufacturing technology to make donut shapes that small? if so, i bet we can make spheres even smaller to the point that there is a size at which we can make spheres that we cannot make donuts.
The first atrocity they committed was reusing the variable "R" for both shapes' radii when they are clearly not equal. and having them side by side, have they never heard of subscripts?
secondly, depending on that actual size of each, it may be possible their spheres beat out the donuts.
third and lastly, this also isn't a simple surface area to volume question, as the glaze has thickness and that thickness will be affected by the geometry of which its applied. when coating a sphere, its not simply the surface area multiplied by the thickness. its the volume based on the final radius of the coated sphere minus the volume based on the radius of the uncoated sphere, the volume of glaze increases as the thickness increases. but for the donut shape, once the center hole is filled, you have intersecting glaze of which you cannot double count, assuming glaze is handled at constant thickness, but in the real world glaze tends to collect in thicker amounts based on geometry, like how some glazed donuts might end up having sealed off holes with a much larger volume of glaze captured than it would have under assumed nominal thickness coating.
Would a nearly fractal, three dimensional object that stops fractalization (or whatever the technical term is) at a point where the distance between two fractal faces is twice the glaze thickness maximize the amount of glaze on a single object?
For a volume of multiple objects, like cereal, presumably you would want a fractal-like shape that fills the volume completely, like a cube with holes? Or would the likelihood of an inefficient orientation in a box make a fractal that was closer to a dodecahedron be more efficient on average?
I think you're describing a sponge. Sponges are pretty good at soaking up water, the worst kind of glaze.
A donut + a sphere delivers more glaze than a donut
The claim does not state a denominator, it never says per volume of batter. It can't be false or true
The claim is about shapes though. OF COURSE having two of the thing is more opportunity for glaze than having just one of the thing. Having three would be better yet.
Woh, imagine a whole boxful! They're genius...
I think the direction is clear: spheres of glaze covered in a thin coating of fried dough.
“…by 2050, glaze-by-the-gallon vending machines were in 38 countries…”
Tbf it doesnt say it's a way to deliver more glaze. It says its the perfect shape to do it.
So really it is false.
Your statement is the embodiment of everything that is wrong with modern advertising.
Glaze fight!!!!! 👊🏼
Lol that’s really pedantic
And still untrue. The statement is about shape to deliver more icing and the shape obviously is the limit, so there’s no argument it’s correct
💯 like I guess there could be a million orbs stuck together by one molecule but that’s not cereal
No, look closely at the formula they give for a torus. 2piRr, even though the usual formula for a torus’ surface area is 4piRr. They are assuming that the torus’s top half is glazed but that its bottom half is bare, but they assume that the entire doughnut hole is glazed. With these assumptions, they are correct.
Wait, isn’t the total surface area of a torus (2 pi R)*(2 pi r) or 4 pi2 R r ? In that case, for the torus’ surface area to be greater:
4 pi2 R r > 4 pi R2. Or R / r < pi
If they’re assuming only half the torus is frosted, then:
2 pi2 R r > 4 pi R2. Or R / r < pi /2.
Look at the equations in the box. It’s assumes that R is the same. For that constraint, the sphere has more surface area (under reasonable assumptions). Everyone’s Melvining out over spheres being minimal surfaces and ignoring the common sense aspects of this that make it true
If we use this interpretation, then the best way to get more glaze is to just make bigger donuts. Double the volume of dough and you'll increase the amount of glaze you can put on it. But that's a trivial solution that doesn't require any math. And this isn't an optimization problem anymore. It's a scaling problem. How big can you make a donut? Well, cost and psychology and demand will put constraints on that, but math doesn't. The only mathematical optimization that makes sense is how much glaze per volume of dough. And spheres are mathematically the worst.
Nope. Even if R is the same, the donut comes out ahead of the sphere, because pi > 2.
2*(pi)^2 > 4*pi
What if r << R?
This isn’t equivalent to what’s on the box. You’re ignoring r
In your comment you said "It assumes that R is the same", so R^2 = R^2? if not, what did you mean?
Sorry. I’m sick so I’m really half assing these comments. I mean "for a given R, fixed to be the same across both equations, and a reasonable r, this is true"
Presumably, unreasonable values of r make impossible shapes?
Yea. It includes them. A good example is degenerate spheres (where the torus becomes a double covered sphere)
Id argue that a sphere would be the worst possible shape when it comes to surface area to volume ratio. While the ideal shape would be an infinitely complex fractal, such a shape would have infinite sugary glaze compared to its finite volume such sugary perfection we could only ever hope to achieve in the science of sugary confectionery.
So what you're saying is we need Gabriel's horn shaped cereal for infinite glaze per unit volume.
Seems like they found a critical point without doing a second derivative test
I think you have interpreted incorrectly. To me this is saying a doughnut with a hole has more glaze than a spherical doughnut.
[deleted]
Hey the picture says that the whole in the donut shape makes it more suitable for glazing and also has an arrow pointing at the torus to signify that it's better.
I find no way to interpret this as saying that the sphere is actually better. But everyone acts like it does. So what am I missing???
I came here to say this. If you want the least glaze, you want the smallest surface area, which means a sphere. Cubes are pretty good too.
Marketing people all failed math
Succeeded in marketing though
It's perfect because it's the most efficient. They don't want to deliver more you you. That costs money. The joys of late stage capitalism.
Its surface area not volume that's why its squared not cubed.
The sphere surface area formula is correct.
The torus surface area is wrong though I believe it should be 4(pi)2 Rr
Maybe there’s no glaze at the bottom just in the top half 🙂
It looks like they actually did the math
…you know, I bet this is the real answer. They glaze the whole doughnut hole but only glaze half the doughnut
So they've mathematically proven they're inferior to Krispy Kreme because they can't figure out how to glaze a whole donut.
I think that any conclusion pointing to the perfection of Krispy Kreme is demonstrably true
Damnit now I'm going to have to hop in the car and grab a half dozen
For science!
Awesome
But glazed donuts are always glazed all over. Only things like chocolate dipped are 1 sided. It's like those icing sugar donuts my friend!
That certainly isn’t true historically.
That’s still not the ‘best’ answer. It’s better than half a torus (EDIT: some tori), sure. Why the best? Why not point out it’s better than a flake where you just put a tiny dot of glaze in the middle? I mean sure.
Well the difference is obviously because a standard doughnut is half glazed
My man has not been to a Kristy Kreme!
😂 I do appreciate the K.K. style of glazed doughnut
But that’s a random comparison between two possibilities, and not simply about the choice of shape, as they claim, but the dumb choice to only do half of it. This specifically says the sphere is the ‘perfect shape’ across the board.
Well not if maximizing glaze on donut. (Like Krispy kreme)
Have this: π
I wouldnt be surprised if its a test to find out if they dumbed us down to the point of no one knowing geometry and if we know the equations for the surface area for a torus/if we would question it. Im guessing rn, a torus is a known geometric shape by the general population that paid attention in geometry, but that won't be the case in the future. It's one of those things that we think doesn't matter until it does. Corporations want to find ways to implement shrinkflation as much as they can, and tricking taste buds with flashy advertising is a good way to do it. Im still pissed with Jose Ole taquitos filling becoming pathetic and then the introduced "stuffed" taquitos. I bought the stuffed ones to see if it was what I remembered and stopped buying taquitos altogether. They can trick my taste buds, but they can't trick my stomach.
Theres a guy who emailed them to complain and they actually responded. He got some boxes of cereal out if it
Also when i saw these in the store earlier this week they'd removed the bad math and claim from the box
"We did the math." Turned into "we didn't do the math and had to recall a mistake before we got 500,000 calls."
We got the math backwards
In my head, they saw a=4 is bigger than a=2 and stopped reading and didn't do the math to see what's bigger.
They couldn't have just walked down to the plant floor, found an autistic and pedantic engineer for the real answer before going to print?
You think salespeople have the slightest clue that anyone could possibly be smarter than them?
Except pi is bigger than 2 so youre taking it from 22pi to 2pipi
Prove it
Well you see, 3 is bigger than 2.
You can't just say things and have them be true.
pipi teehee
:)
In my head, you saw I said a=4 is bigger than a=2 and stopped reading.
Hey, that's weird. That's what you did in my head.
Yeah, we’ve been there, done this already (I remember cause I left some half assed comment about fractals and it was by far the most upvoted comment I’ve ever had in my life)
According to your profile this is your most upvoted comment
https://www.reddit.com/r/interestingasfuck/comments/1p0qj7x/comment/nplipex/?context=3
And this is your most upvoted comment in this
https://www.reddit.com/r/theydidthemath/comments/1pj9p6z/comment/ntbw5hv/?context=3
Where is your fractals comment?
Sorry, I’ve apparently gotten so much more popular since then. Didn’t mean to be purposely deceptive, and also still don’t know how to copy/paste links to other Reddit posts
That okay, I was just looking for it, that is all.
This has been posted multiple times, and one person even sent a letter/email to them about this. Iirc, there response was that for a given amount of glaze, a sphere results in the thickest coat which is true but not quite what it says on the box
Wouldnt that just be saying the surface area on the sphere is less?
Pretty much, and that is rhe equation on the box, at least for the sphere
Here it is for reference. https://www.reddit.com/r/theydidthemath/s/HxUQ00nmUs
But the box says that the Torus is the superior shape why would they defend the sphere? It says the the hole in the donut shape makes it more suitable for glazing. So they should stick with that?
Pretend lawyer here. It could be argued that what is meant by "deliver" describes the ratio of glaze-per-bite. A single bite sphere has more surface area than a cylindrical cross section bite, and therefore "delivers" more glaze.
Discuss
This is a cereal, so another interpretation (which imo is what they actually mean given the context) is the total amount of glaze that would be present on a spoonful of each shape. So like factoring in how each shape behaves as a granular material.
What is the optimized packing of oblate spheroid grains in a well-ordered lattice of milk? Does this hold true when we extend to such fields as "the taste is in the shape, Honeycomb!" ?
This is what I was thinking. It delivers the most glaze per amount of donut, so it has the best efficiency at glaze-delivering.
It actually has the least glaze per amount of donut. But, it could cause you to eat more donut per bite if the sphere is larger than your typical bite but too small for you to want divide it into two bites
You would be correct Colonel O'Neil.
However they may be calculating this number based off of the donut hole and the donut being the same size. In which case the sphere would have more area given the donut is but a fraction of its volume even if the donut has more area per volume.
Sadly my mathpertise doesn't extend to objects that are round. Perhaps Daniel Jackson or Major Samantha Carter would be able to answer your cereal problems better.
Thought i had a stroke. What is the SG1 connection that im missing?
Jack O'Neil rarely mentions anything more than once across the series but he routinely has critique's around cereal throughout the show. Fruit loops, wheaties, questioning the worth of certain cereals, etc. I figured I'd hit one SG1 fan in the nostalgia bits by answering as if this was Jack O'Neil (Neal?) asking another cereal based question
Ah okay. A little bit too deep of a cut for me to catch.
Its O'Neill (two Ls) ;)
Also, it's Lt General O'Neill. He's gotten a promotion or two.
Maybe the donut looks like a stargate? Feels like a stretch but I don't see any other connections either.
Depends on the value of little r
Example: R = 10 r = 1
A(sphere) = 4pi ×100 = 1256
A(Torus) = 2pi2 × 10 × 1= 197.2
Example 2: R = 10 r = 9
A(sphere) = 1256 still
A torus = 2pi2 * 90= 1774
I think it’s safe to assume that r ≈ R/2
Depends on how they define “more glaze.”
If I have one unit of liquid glaze to put on one unit of cereal, spheres are going to result in thicker layers of said glaze. If that’s what’s desired, then spheres are going to be the best option.
A torus is only “better” if you have a predefined glaze thickness you’re looking for.
Haven’t done the math again…but would this ratio remain the same as long as both objects have the same cereal volume?
No. I fact if the sphere had the same volume that guarantees the surface area is smaller for the sphere than every other possible shape. It is only if the sphere has
lessmore volume than the torus that its possible for the torus to havemoreless surface area.Edit: less is more
It depends on R and r. The sphere has more surface area if R > pi * r / 2. So if R is say 1.6r then sure its true, but if R is 1.57 r then it's false. All of that is assuming the R for the sphere and the R for the torus are the same R (which I think is a fair assumption).
Actually I just googled the surface area formula for a torus and they made a mistake on the box. It should be 4 pi² Rr so the adjustment to my answer would be it's true if R>pi r
You correctly point out that a sphere is the worst possibly shape to maximize glaze
The best shape would be 2 dimensional plane which would have infinite surface area to volume.
Did the math a few months back. Reposting my comment.
Unnecessary detail to follow: Using the equations for surface area they show, we set them equal to each other to determine the breaking point.
4πR² = 2π²rR 2R = πr 0.67R ≈ r
R is the radius of the donut hole, and the large radius of the donut. r is basically ½ the thickness of the donut. So a 5" donut needs a hole smaller than 1" to have a larger surface area. It basically needs to be a super thick donut.
Now, this is ignoring the volume. Let's assume the same volume
4πR³/3 = 2π²rR² R = 3πr/2
4πR² → 6π²r 2π²rR → 3π³r² 6π²r = 3π³r² 2 = πr 0.67 = r
So, assuming they both have the same volume, any value of r greater than 0.67 gives the donut a larger surface area, and any value less gives the sphere a larger surface area. Plugging it back in to make more sense, the ratio R:r needs to be less than π:1. Any higher higher than that, say 4:1, and the donut hole will have a larger surface area. This ratio equates to a 5" donut with a 2.5" hole, which isn't actually that crazy.
So I guess in a lot of cases, they might be right... Anyone wanna double check my math? Doing all of this from my phone :P
To get a real comparison you would probably want to do the surface area : volume ratio between the two shapes and whichever is greater is theoretically the better deliverer of glaze.
A sphere is the 3D shape with the lowest surface area per volume. It's a defining characteristic of spheres.
Literally any other shape would have more glaze
The torus area should be 4pi2 rR, but isn't that weird? That's just the circumferences of the two circles that make up the torus multiplied together, which is a bit surprising since the inwards facing side obviously has a lower area than the outer one. Intuitively I would think the area would be a bit bigger than that?
I guess it's another one of those things where the linearity of it just makes it work out, like the area of a circle being the average length of the infinite concentric circles it would take to fill it (pi r) times their number (r)
As a professional level donut and Timbit (donut hole) glazer, I can accurately state that the donuts use up more glaze than their counterparts.
The only exception to that is the volume of product sold. In general, Timbits are sold more often and more types of them are glazed than donuts.
This reminds me of a legendary discussion between two icons in regards to the theoretical shape of our universe.
Over pints of beer, no less!
First of all, a toroid's surface area is 4π²Rr. Second, yeah a donut hole will have more surface area if it's somehow LARGER than the donut it came out of.
The bar is on the floor. "We deliver more glaze per unit volume than literally the worst possible shape for delivering glaze per unit volume." You know what would be better than a torus, Frosted Flakes? A goddamn flake!
Inb4 some fractal monstrosity with zero surface area somehow proves me wrong.
https://www.reddit.com/r/theydidthemath/s/tmbaZGFTLN
https://www.reddit.com/r/theydidthemath/s/WNjpYY6nam
https://www.reddit.com/r/theydidthemath/s/pBeBejeTbl
https://www.reddit.com/r/theydidthemath/s/XxlHMbV1re
Literally identical posts ranging from 1 to 11 months ago....
Y'all, just try the search function.... PLEASE!
I think this is hilarious. Like somehow the sphere. is the optimal shape per amount of thing called R. Cause it’s certainly not per volume lmao
Here's a good way to look at it, if you poked a holed in the middle of the donut hole to utilize more potential glazing surface area, would that be a regular donut?
Copyeditor here: What if they’re just tragically misusing the term “donut hole,” which most would consider a spherical donut ball, to refer to the hole of the donut. Thus, they mean the donut shape is better. My evidence is the arrow points to the donut (right) more than the donut hole (left being the spherical donut).
Well I’m too tired to do the math, but if you keep the volume of them the same, then yes, I believe that the regular donut would have more glaze than a circular ball, but if you for instance made donut balls the same thickness as the donut is all around, then you would be getting more glaze(picture one donut, and then let’s say 6-10 small donut holes in a circle that equals the same thickness. You would have more glaze - if you broke a piece of the normal Donut off the same size as the holes, they’d be the same size, but two sides wouldn’t be glazed.
So I guess it depends if: A of donut hole = A of donut.
Hey the picture says that the whole in the donut shape makes it more suitable for glazing and also has an arrow pointing at the torus to signify that it's better.
I find no way to interpret this as saying that the sphere is actually better. But everyone acts like it does. So what am I missing???
Am I going crazy? Why is everyone acting like this???
I think you’re missing the point here. If you compare a sphere with a donut shape of the exact same size, then yes, the donut shape has more surface area. But if you take a bit sized section out of that donut shape, that is equal to the same size as the donut hole, the donut hole has more glazed surface area because the donut bite has no glaze on the sectional surface. The bite is a tube with no glaze on the sides. So a box of donut holes has more glaze per box, than a box of donuts.
But yes, their math is dumb…
Am I missing something? I assumed all the answers would say it depends but haven't seen that at all. Also, the equation for the torus is incorrect, it should read 4Rrπ2. With that being the case we can equate and simplify the equations (assuming all variables have the same value) to:
R = πr
Thus which one has the biggest surface area of course depends on the radii. Seeing as no radii are common to both sides once simplified, we cannot say for a given R which one would have a bigger surface area.
Edit: fixing some formatting by sticking π at the end of the torus equation. Didn't realise Reddit would superscript!
Please help, why all the people just say "they re wrong sphere is the worst shape to deliver more glaze" and the text is "donut is the perfect shape to deliver more glaze", don t they mean that the sphere isn t the perfect shape? What do I miss?
As for math I have no idea, but as a 3D artist...
WHY IS ONE OF THE LOOPS IN THE DONUT VISIBLE ALL THE WAY THROUGH AND THE OTHERS AREN'T?
DO WE HAVE VIEWPORT TRANSPARENCY ENABLED OR NOT?
It's directly opposite. A toroid has more surface area. That's why they put the hole in the donut in the first place, so there isn't a ball of raw dough in the middle after frying.
A sphere is anyway the smallest area possible out of all shapes for a set volume, so no matter the form of your donut I guess, it would always be better than a sphere
IANAL but I'd argue the language intends to say "the perfect shape to deliver more glaze than we have previously, not more volume of glaze per unit, and the benefit to the customer is in volume of product - with glaze being the most expensive part, by spreading it thinner on each hole, we are able to give more holes at lower cost."