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7 members have voted
Let me introduce some pictures I took myself at the local supermarket.

Front of box

Back of box.

Math equations on back of box.
So, Kellogg's has introduced spherical shaped versions of Frosted Flakes, Apple Jacks, and Krave (which I never heard of before).
The back of the boxes claim that the spherical shape is "genius" because it delivers more glaze. I assume they mean the ratio of surface area to volume is greater comparing the sphere to a torus (donut shape).
Before going further, let's review the formulas for volume and surface area for both shapes.
Sphere:
Volume = (4/3)𝝅r3
Surface area = 4𝝅r2
Torus:
Volume = 2𝝅2r2*R
Surface area = 4𝝅2r1*R
where r = radius of the circle that is rotated 360 degrees around the center creating the torus, R = distance of torus from center
In the case of the torus, r represents the radius of the red circle as shown in the following image.

On the back of the box, the A clearly refers to surface area.
However, their formula has a 2 instead of a 4. Why? Perhaps they think they glaze only half of torus shaped cereals like Apple Jacks or Fruit Loops. However, they don't. It's obvious from looking at classic Fruit Loops or Apple Jacks they glaze the whole thing.
Let's do some math to determine the optimal shape of cereal to maximize glaze.
If we have a torus with r=1 and R=1, we get:
Volume = 19.7392088
Surface area = 39.4784176
Ratio surface area to volume = 2
Next, let's carefully choose a radius of a sphere to equalize the volume.
Sphere with r=1.67653921
Volume = 19.7392088
Surface area = 35.32134996
Ratio surface area to volume = 1.78940044
With 2>1.78940044, I have shown that a torus delivers more glaze than a sphere.
However, in all fairness, if torus were only glazed half way, the ratio of glaze to volume would be 1, in favor of a sphere.
However, again, they don't just glaze half their torus shape. I submit for your consideration that Kellogg's didn't do their math correctly.
In fact, I submit that the Isoperimetric Inequality says the sphere actives the LOWEST ratio of surface area to volume.
I still have more to say on this topic, but that is enough for one post. I'll close with some relevant links.
Isoperimetric Inequality
Torus
Internet spots big mistake on Kellogg's cereal box
Stellated Octahedron (I'll get to this one)
The question for the poll is what shape of breakfast cereal achieves the most glaze?
That's all I got
Quote: JohnzimboSorry, I like the shredded wheat mini pillows.
That's all I got
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Aren't they only frosted on one side?
Honeycomb was another, I thought. One side seemed shinier.
Quisp, on the other hand, seemed to be predominantly sugar glaze or glaze-equivalent, bound together with the bare minimum amount of grain to maintain structural integrity.
An infinitesimally thin flake will yield an infinite ratio of glaze/cereal.
I voted flake. But I’m kind of curious to know how a fractal would be different from a flake. At least for this exercise, anyway.
But regarding the original question, isn’t it relatively well known that a sphere is the best shape for maximizing the volume to surface ratio? Therefore, it would seem to be the worst candidate for an area to volume ratio. Clearly, even without the math, it would seem that the torus is better than the sphere.
Mike, if I was you, I’d write a very strongly worded letter to Kelloggs. 😡
At another one to whatever federal organization is involved with truth in advertising. That is, assuming that Trump hasn’t dismantled it. 😵💫
Here is an image of Apple Jacks close up, which I think shows they are frosted on both sides.

Image source: https://commons.wikimedia.org/wiki/File:2020-05-03_09_34_31_A_sample_of_Kellogg%27s_Apple_Jacks_cereal_in_the_Franklin_Farm_section_of_Oak_Hill,_Fairfax_County,_Virginia.jpg
In particular, I use a tetrahedron as a starting point. The first step would take us to a stellated octahedron.

The following table shows the volume and surface area for the first 20 fractal iterations.
Level | Volume | Surface area | Ratio SA to volume |
---|---|---|---|
1 | 0.117851 | 1.732051 | 14.696938 |
2 | 0.176777 | 2.598076 | 14.696938 |
3 | 0.220971 | 3.897114 | 17.636326 |
4 | 0.254116 | 5.845671 | 23.003904 |
5 | 0.278976 | 8.768507 | 31.431076 |
6 | 0.297620 | 13.152761 | 44.193114 |
7 | 0.311603 | 19.729141 | 63.314899 |
8 | 0.322091 | 29.593712 | 91.879989 |
9 | 0.329957 | 44.390568 | 134.534586 |
10 | 0.335856 | 66.585852 | 198.257286 |
11 | 0.340280 | 99.878777 | 293.519244 |
12 | 0.343598 | 149.818166 | 436.026868 |
13 | 0.346087 | 224.727249 | 649.337067 |
14 | 0.347954 | 337.090874 | 968.780691 |
15 | 0.349354 | 505.636311 | 1447.347971 |
16 | 0.350404 | 758.454466 | 2164.516810 |
17 | 0.351191 | 1137.681700 | 3239.495213 |
18 | 0.351782 | 1706.522550 | 4851.084900 |
19 | 0.352225 | 2559.783824 | 7267.476620 |
20 | 0.352557 | 3839.675736 | 10890.942993 |
21 | 0.352806 | 5759.513605 | 16324.877603 |
22 | 0.352993 | 8639.270407 | 24474.353438 |
23 | 0.353133 | 12958.905611 | 36696.960326 |
24 | 0.353238 | 19438.358416 | 55029.060808 |
25 | 0.353317 | 29157.537624 | 82525.173666 |
Quote: DJTeddyBearI haven’t eaten frosted flakes lately, but I kinda think that a flake, even if it’s only coated on one side, would offer the greatest surface area to volume. But I wonder how the thickness of the flake would come into play.
I voted flake. But I’m kind of curious to know how a fractal would be different from a flake. At least for this exercise, anyway.
But regarding the original question, isn’t it relatively well known that a sphere is the best shape for maximizing the volume to surface ratio? Therefore, it would seem to be the worst candidate for an area to volume ratio. Clearly, even without the math, it would seem that the torus is better than the sphere.
Mike, if I was you, I’d write a very strongly worded letter to Kelloggs. 😡
At another one to whatever federal organization is involved with truth in advertising. That is, assuming that Trump hasn’t dismantled it. 😵💫
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It is true that bubbles are spherical, as their surfaces contain the greatest volume using the least surface area. (Or as DJTB said, “…maximizing volume to surface ratio…”)
@Wiz, Good catch! Give ‘em hell!
ETA: I voted flake, but I haven’t done the math on any shapes outside of math classes taken decades ago.
I also checked “I’m a bigot”, as I’m bigoted against bigots. Talk about a recipe for self loathing…
I would say that is self evident, however, somebody had to do the math to prove it and I thank you.Quote: WizardIn fact, I submit that the Isoperimetric Inequality says the sphere actives the LOWEST ratio of surface area to volume.
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the audacity for them to post a formula and claim it 'proves' what they say is outrageous
I say it smacks of girl math!!

(weirdest sentence I've made all week)
Perhaps they know what they are doing, which is simply selling cereal.
Quote: WizardI've already spent hours on math behind this post, which will mean it will probably get very little traction. However, I'm used to it. Probably explains why 97% of women find me incredibly boring.
Are you sure, only 97%?
Quote: WizardSo, Kellogg's has introduced spherical shaped versions of Frosted Flakes, Apple Jacks, and Krave (which I never heard of before).
I think Krave is chocolate "pillows" filled with some sort of vanilla creme. Spherical ones would be like "creme-filled Cocoa Puffs." It is one of its newer cereals.
Quote: WizardHowever, their formula has a 2 instead of a 4. Why? Perhaps they think they glaze only half of torus shaped cereals like Apple Jacks or Fruit Loops. However, they don't. It's obvious from looking at classic Fruit Loops or Apple Jacks they glaze the whole thing.
I have a feeling they meant to say (2𝝅)2Rr instead of 2(𝝅2)Rr
Quote: ThatDonGuyQuote: WizardSo, Kellogg's has introduced spherical shaped versions of Frosted Flakes, Apple Jacks, and Krave (which I never heard of before).
I think Krave is chocolate "pillows" filled with some sort of vanilla creme. Spherical ones would be like "creme-filled Cocoa Puffs." It is one of its newer cereals.Quote: WizardHowever, their formula has a 2 instead of a 4. Why? Perhaps they think they glaze only half of torus shaped cereals like Apple Jacks or Fruit Loops. However, they don't. It's obvious from looking at classic Fruit Loops or Apple Jacks they glaze the whole thing.
I have a feeling they meant to say (2𝝅)2Rr instead of 2(𝝅2)Rr
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If they correct the math, watch for the early box versions to soar in value.
Specifically I wonder whether "surface area/volume of shape" is the correct figure of merit. Instead, I imagine that the correct figure of merit is "surface area/volume that the shape occupies."
Given that you have a cereal bowl that will be filled with liquid milk after you have put the glazed cereal shapes in the bowl. The cereal shapes are a "delivery system for sugary glaze." You want to maximize the surface area of all the shaped cereal in a bowl of fixed volume.
A torus may have more surface area than a comparable sphere, but the torus would (I think) occupy more volume in the cereal bowl. Because the hole in the torus is inefficient. Thus the ratio of 'surface area to volume occupied' of the torus seems like it might be lower for a torus than for a sphere.
Rigorously, the packing density of the shapes might be a consideration as well. I really haven't considered packing density.
Quote: gordonm888
Rigorously, the packing density of the shapes might be a consideration as well. I really haven't considered packing density.
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(My Ai generator kung foo is weak)
Quote: rxwineQuote: gordonm888
Rigorously, the packing density of the shapes might be a consideration as well. I really haven't considered packing density.
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(My Ai generator kung foo is weak)
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I think I need to trademark that name. Then my commercials would feature people trying to say "Wute Cubes" 3 times fast.
Real sugar is a large molecule and can produce some strong forces with other surfaces which is why it is so sticky. So it won't flow into an extreme fractal. Another funny thing that happens is substrates and coatings stress each other. This is a problem in optical design because if you coat a thin element on one side, the resulting stress from the dissimilar materials being in contact will bow the substrate so that it's not optically flat anymore, and the usual remedy is to coat the other side too, with a coating that will produce an equal stress at all temperatures the finished product will experience. If you were to coat only one side of a corn flake with sugar, it would probably crack the flakes over time and you could end up with a box of Crumbly Mess cereal.
So for the best way to do it with a real-world product, I'll go with what I knew as a little kid- that Sugar Frosted Flakes are the best because they have the most sugar, and even after the scoundrels changed the name to mere "Frosted Flakes" we all still knew.
The general rule was that sugar had to be the fourth ingredient or later, but it wasn't set in stone.
We were a Special K family, but switched to Total when that came out, as I recall.
Quote: DRichAre you sure, only 97%?
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No, I'm not. It was an optimistically low estimate.
If there is any value to the starch part, first decide what ratio is best, then decide which shape best achieve that. Since today is Memorial Day, where we honor those who gave their lives in defense of corporate profits, I suggest we test a bunch of them and see which ones sell the best.
I voted for flakes because, in addition to the reasons mentioned above, the irregularity of the flake's surface provides more area for the glaze to accumulate.
On the subject of cereal disinformation, was anyone else as devastated as I when they found out that
Quote: Joeman
On the subject of cereal disinformation, was anyone else as devastated as I when they found out thatare all the same flavor, regardless of the individual loop's color!
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I was only mildly surprised. My recollection of Froot Loops is that they are only glazed on one side.
Quote: Dieter(snip!)
Quote: Joeman
On the subject of cereal disinformation, was anyone else as devastated as I when they found out thatare all the same flavor, regardless of the individual loop's color!
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I was only mildly surprised. My recollection of Froot Loops is that they are only glazed on one side.That's still what, 60 million broadly age appropriate you could talk to? I simply don't have that kind of time.
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Is that where the practice of calling women “broads” came from?