---
title: 'When maths marketing goes wrong.'
source: 'https://youtube.com/watch?v=CYjD9cpxT18'
video_id: 'CYjD9cpxT18'
date: 2026-06-28
duration_sec: 0
---

# When maths marketing goes wrong.

> Source: [When maths marketing goes wrong.](https://youtube.com/watch?v=CYjD9cpxT18)

## Summary

The video critiques a Kellogg's cereal box that uses mathematical equations to argue that spherical donut holes deliver more glaze than torus-shaped donuts. The host identifies a typo in the torus surface area formula and unpacks the marketing claim, ultimately agreeing that spheres provide a thicker glaze layer when the same amount of glaze is applied to equal volumes of cereal.

### Key Points

- **Initial Reaction to Cereal Box** [0:00] — The host expresses major issues with the back of a cereal packet, highlighting a confusing mathematical diagram and equations.
- **Blueprint Effect and Typo** [1:01] — The box features a blueprint effect on 3D objects. There is a typo in the torus surface area equation: a '2' instead of a '4', which the host calls the mathematical equivalent of a typo.
- **What is a Donut Hole?** [2:22] — The host explains that Dunkin Donuts' marketing gimmick sells the dough punched out from donuts, though in reality, donuts are formed as rings. A video shows a machine stamping donuts from a sheet, leaving dough in the middle.
- **Glaze and Shape Comparison** [4:09] — The host compares a glazed sphere (donut hole) to a glazed torus (donut), noting that the sphere in the picture is larger than the torus, so the comparison is not to scale.
- **Mathematical Flaw in Marketing** [6:21] — The claim 'donut holes are the perfect shape to deliver more glaze' is mathematically backwards: a sphere minimizes surface area for a given volume, so it delivers the least glaze, not the most.
- **Kellogg's Response from Reddit** [9:52] — A Reddit user contacted Kellogg's, and Connie from consumer affairs explained their logic: for equal cereal and glaze mass, the sphere has less surface area, resulting in a thicker glaze layer.
- **Agreement with Kellogg's** [13:42] — The host agrees that if 'more glaze' means thicker glaze, Kellogg's is correct. The sphere builds up a thicker layer of glaze when the same amount is applied to equal volumes.
- **Practical Demonstration with Cakes** [14:36] — The host bakes a hemispherical cake and a half-donut cake with equal cake volume, then applies the same amount of icing. The sphere ends up with a much thicker icing layer, confirming Kellogg's point.
- **Encouraging Maths in Marketing** [18:37] — Despite the typo and poor wording, the host praises Kellogg's for including maths in marketing aimed at children and encourages them to fix the typo and improve phrasing.

### Conclusion

Kellogg's marketing claim, though poorly worded and containing a typo, is mathematically valid if 'more glaze' means a thicker layer. The host encourages more maths in marketing and urges Kellogg's to fix the typo.

## Transcript

I have some major issues with this cereal packet. 
Imagine you walk into a supermarket, you look at
the cereal section, pick up a packet, and on the 
back of it, you see this. I don't have an issue
with the front of the box. I have a major issue 
with the back of the box because as well as Glazed
is genius. Hang on, let me bring it over here. 
They've put Look at this. Look at that nightmare.
What is this? We did the math. Donut 
holes are the perfect shape to deliver
more glaze. The area of a sphere equals 
4 pi r². The area of a taurus equals
uh 2 pi squar r r r r r r r r r r r r r r 
r r r r r r r. Max glaze equals max flavor.
Oh yeah, I um printed them out.
Okay, things we have to deal with straight away. 
First of all, putting a blueprint effect on a 3D
object. I don't know what's going on there, but 
they are they're fun objects. I got to give it to
Kelloggs in that regard. Um, there is a typo. So, 
they've got two equations there. One is for the
equation of the surface area of a sphere. That 
is correct. They've also got the equation for
the surface area of a Taurus, which features pi 
squ. Very nice. That's why pi is better than to
tao. And they put it in brackets for no obvious 
reason. I can forgive that. And they put a two
instead of a four. That's harder to forgive, but 
it is the mathematical equivalent of a typo. Like
I wish they would fix it. If they had a spelling 
mistake, they would have fixed it. And people have
been putting this out for a while that they've got 
a two instead of a four and they haven't changed
it. So I am annoyed at that. But it is a little 
trivial. More important are the mathematical
problems with the whole concept they're trying 
to get across. And oh, by the way, I'm not the
first person to get annoyed at this box. Other 
people have done that, but we do have some new
information. Very exciting. Get to that in a 
moment. All right, but the point is people are
annoyed at just the maths. And I showed this to a 
few other mathematical friends of mine. Everyone
got annoyed for subtly different reasons. And so I 
thought we just have a quick quick chat about what
Kelloggs could mean and eventually what they do 
mean right off the bat. What is a donut hole? The
void in the middle of the donut. Well, here's the 
thing. A while ago, Dunkin Donuts did this thing
where they, as a marketing gimmick, sold the dough 
that would have been the holes in the donuts when
they get punched out. And actually, I've scaled my 
models to represent that in theory, this is meant
to be the hole from the middle of a donut, but 
it's like the hole, the bit that's removed to give
you the hole. And a lot of people think that's 
ridiculous, myself included, until quite recently,
because that's not how you make donuts. You just 
make a ring of thing and your machine puts it in
some boiling oil or something. So, there is 
there is no dough in the middle. But then we
looked it up. Producer Nicole found this a video 
of the machine that makes the donuts for Dunkin
Donuts because obviously that's happening at some 
ridiculous scale and they start with just a sheet
of doughut ooze and then they stamp out donuts 
leaving behind dough in the middle. So there is
dough from the doughut holes. Now whether or not 
that dough actually becomes the doughut holes they
sell feels very unlikely. I imagine it just gets 
mushed back in again. I mean, what about the dough
in between the donuts? I don't see them selling 
doughut manifolds, like the leftover joiny bits.
I'd buy that. What a delicious snack. You could, 
you know, distort it, make it hyperbolic. Anyway,
the point is the gimmick was it's the dough from 
the middle. In reality, they actually do have
dough in the middle. I don't think they actually 
just cook that as holes. But that's why now in
American cuisine there is the notion of a donut 
hole just being a fancy way of saying an edible
sphere. The second part of the name we need to 
unpack is glazed. So Kells haven't just got donut
holes, they've glazed them, as I believe the kids 
say. So, this um is is a sphere that they're going
to put this kind of pure sugar all over. And then 
this is a Taurus or a donut that they're going to
put pure sugar all over. And they're trying to 
argue that the sphere is superior to the Taurus
when you're smearing a sugary glaze on it. And 
the ones I've made, you think, well, hang on, just
very naively. No, if this was the donut and that's 
the center to scale, that's got way more area.
Like, if you had to glaze all of this, that's way 
more glaze than the sphere. So, that's that's not
what we're talking about. In fact, the picture 
um the the sphere is bigger than the Taurus. So,
we can already accept that no, we're not talking 
about to scale the literal hole out of the donut.
But does that mean maybe big R is the same? 
Because the big R appears in both equations
and you could solve for that like if you solved 
it and it was like pi on R, then you would have
the same area for both. And if it was any bigger, 
you'd have more area on the Taurus. Any smaller,
more area on the sphere. But that's just it's a 
fancy way of saying bigger things have more area
to a certain extent. It depends obviously on the 
shape. Um and that's that's something to be said.
Um but I don't think I don't think that's what 
we're talking about. I think the Rs in each of
the equations just represent that radius of 
that object. Like we're not assuming the A's
are the same. And when you look at a big list of 
equations for areas of things, you don't go, "Oh,
they must all have the same height or whatever." 
It's just that R pertains to that object. So,
I think what we're actually talking about is just 
comparing the concept of a sphere to a donut.
Finally, we're going to get to the point a lot 
of you have been yelling at your screens from the
very beginning of this video because they say, "We 
did the math. Donut holes are the perfect shape
to deliver more glaze." And you've been yelling, 
"No, they're the perfect shape." mathematically,
rigorously to deliver the minimum amount of glaze. 
Because famously, a sphere is the most efficient
way to maximize your volume, the amount of cereal, 
and minimize your surface area, the amount of
glaze. So, it's the exact opposite of what they're 
saying. If you wanted to minimize the amount of
glaze you need, you'd go spheres. If you want more 
glaze, you want a more complicated shape like a
Taurus. Now, side fact, proving that a sphere is 
the optimal 3D shape to minimize surface area to
volume. Non-trivial. I think it was like the 
1970s. We I'll put a picture of the paper up
somewhere, right? Like complicated. And we'll 
link to that paper if you want to go check it out,
but it is true. This is if you want to minimize 
glaze, that would be the optimal. And actually,
mind your decisions did a whole video about this. 
So I'll link to that below. They look at what
happens when you donutify a sphere and how that 
changes the surface area. But the kind of founding
principle of this argument is that would be if you 
always had the same amount of cereal per cereal.
So, if every piece of cereal is the same amount 
of cereal, and it doesn't matter what shape,
like you've got your your quantum of cereal and 
you're going to turn that into a shape. And for
the record, Kelloggs don't even make loops of 
any form. I don't know why why they're going
on about donuts. They don't do any donut shaped 
cereals. I What's a normal frosted flake? I mean,
guess it's flake shaped. It's like a probably like 
a saddle or something. Anyway, point is if you go,
oh, the machine gives a certain amount of 
cereal per per per thing. What shape should
we mold it into? Sphere is the worst 
choice. But the founding assumption is
equal cereal per cereal. Actually, how 
big are the spheres? It's pretty big.
About yay big.
Max flavor.
The top two ingredients are 
sugar and then air. A sparsely
infilled sphere purely as a mechanism to 
transport sugary glaze into your face.
They somehow as piping submerged in 
milk crumble into dust as you eat them.
I've made some weird career choices. I 
just realized no one's making me eat these.
Just literally eating a bowl of cereal 
while paying someone to film me. Yeah,
you better keep watching.
Now, where this gets interesting is a Reddit 
user Nahan0407, real name I believe Nathan,
reached out to Kelloggs, expressed the concerns 
we all have, and Kelloggs responded. We now have
Kellogg's side of the story. Connie from their 
consumer affairs department engaged with Nathan.
They had a bit of back and forth. I'm going 
to ignore most of the emails. The first email
from Connie lays out their logic behind 
what they've done here. They did not say,
"Oops, you got us." No, they came to play. As we 
considered the shape of our cereal, the sphere is
the most efficient mass to surface area shape. 
Correct? Yeah, we agree. We agree. If anything,
that's the founding premise of why people are 
so upset. The sphere is the most efficient. So,
it's curious that they're establishing what seems 
to be like the silver bullet in their delicious
argument. But there you are. At least we all 
agree on that. Up next. For a given serial piece,
when holding the glaze percentage constant, both 
the sphere and the loop deliver the same glazing
mass and serial mass. Okay, now this one takes 
some more unpacking. This is some weird mashup
of marketing speak and maths babble. Uh uh what 
I think they're trying to say is the the other
assumption we were discussing before if you've 
got the same first of all they're establishing
it's the constant serial per serial. So when 
they're down here saying the same glazing mass
and cereal mass I believe they're saying and 
this will be useful in a moment is that if you
do loops or donut holes it's the same amount of 
cereal in either case. So we were trying to work
out is it oh is it the one that matches etc. No 
they're just saying the volume of the loop and the
volume of the sphere if you're choosing between 
them is the same. Where it gets interesting is
they say it's the same glazing mass. So not only 
are they holding the amount of cereal constant,
they're also holding the amount of glaze 
constant. On we go. The sphere itself has
less surface area than a loop for the same serial 
mass and parocity. They don't. Is that like number
of paws? Are they saying it's absorbent? Let's 
just Okay, let's ignore parocity and just Yeah,
we agree. The sphere has less surface area than 
a loop if it's got the same serial mass. Again,
all on the same page. Closing statement. When 
applying the glazing mass to the serial mass,
why do they keep saying mass? The sphere will 
have a thicker glazing mass application layer due
to the limited surface area in comparison to the 
loop. And there, my friends, is their argument. If
you have the same amount of cereal in both cases 
and the same amount of glaze, if you apply it to
the Taurus, you're going to have to spread it out 
because there's so much area. Whereas the sphere
is the optimal shape to build up the thickest 
layer of glaze possible. And a thicker layer of
glaze is indeed more for some definition of more. 
But that means we did the math. Donut holes are
the perfect shape to deliver more glaze. They mean 
thicker glaze. In that regard, they're right. Now,
we should ignore the fact that they they you can 
just sense them desperately wanting this to sound
as mathsy as possible. They keep referring to 
the the glazing mass and paracity and, you know,
percentages. Like, okay, we appreciate that, but 
all they're trying to say is the glaze is going
to be thicker. And you know what? I I agree with 
them. They're 100% right. And for the avoidance of
any possible doubt, I'm going to take take a leaf 
out of their recipe book. And um we're not going
to we're not going to glaze some loops and some 
holes. Instead, we're going to ice some cakes.
Here's the plan. I'm currently being very uplit 
because I have two mirror like cake plate tray
things and producer Nicole here has first of all 
made a hemispherical cake. That's what flavor is
this one? Uh this is plain plain plain sponge. 
But if I put that on the mirror, look what we
now got. Hang on. Spherical cake. Right. So, we 
have to bake half as much and we get the full
sphere. And more more in a moment on that. We now 
need a donut shaped cake. And so, what do we got
here? This is coffee and walnut. Coffee and look 
at that. Isn't that incredible? And that's half a
half a donut. So, in theory, again, hold that up. 
There's your There's your whole The donut fills
in. It's adequate. Completely adequate. And these 
both have exactly the same amount of cake. Same
amount of cake. There it is as a sphere. There 
it is as as a Taurus or half of each. The math
still works. And finally, we have the frosting. 
So, I'm going to glaze these cakes and I'm going
to put exactly the same amount of frosting on 
both. And to do that, I'm going to weigh the
cakes as I put the frosting on them. How can this 
go wrong? Other than all the obvious ways this is
going to go wrong. Oh, it's got a delicious skin. 
I'm going to have to spread this real thin. I'm
calling it. There we Okay, all I got to do now, 
put the same amount of icing on this here sphere.
So, I think I think we can all agree it's only 
a matter of time before I get the phone call
for Celebrity Bake Off. Imagine this in a tent. 
But more to the point, the process of doing it,
I had to spread the icing way thinner on this 
one. And even then, I mean, around the back,
I didn't even have enough to really do that 
properly. Uh, it was really hard to spread it out.
Exactly the same amount of cake. Exactly the same 
amount of icing. It's on thick as you like. And
now if I cut uh permission to cut these in half. 
If I cut these in half, the crosssection. Okay,
this one I'm going to do in two cuts. Stressed 
the crumb. Oh, it's going to be such a good crumb.
You know, I'm going to do both cuts 
first and then we'll do a big reveal.
So, here we go. Big reveal over here. You can see 
on the Taurus one, look how thin that icing layer
ended up being. And I'm This is me doing the 
best I can to really load it up. Whereas over
here in Sphere Town, look at that. There. So, 
it's a way thicker layer of icing on this. So,
as you can see, the sphere is the perfect shape 
for more. Assuming you're not allowed anymore.
You know what? Kelloggs have convinced me. I'm 
now on their side. They're right. If you want to
have the thickest glaze possible without 
adding any more sugar, and I assure you,
these dose do not need any more sugar. Sphere. 
It's great. thick glaze for no no added sugar
for no more added sugar. You get a thicker glaze. 
They've just worded it very poorly. Like this like
as red is not good and the typo. Fix the t. 
You know what Kelloggs? Fix that typo. And we
have emailed you and you not responded and we've 
just asked you to fix that. Do that. Just fix the
typo and we're cool because I think you've got a 
good point. You just don't have to dress it up in
technobabble language. And more importantly, I 
don't think the rest of us should be dunking on
Kelloggs or indeed any any brand who want to put 
more maths in their marketing. The fact that we
get more maths and culture like this is clearly 
advertised at children, but they're putting maths
there. That's great. We should encourage that 
and we should encourage them getting it right
and fixing their typos and phrasing it better. But 
the point is something is better than nothing. So,
so in conclusion, Kelloggs, your your maths, 
it's not great. But it's it's good. Good work.
Keep it up. Just turn that turn that two into a 
four. Future Mad here. Kelloggs did reply to my
email to say they don't reply to that sort of 
email. So, either they've learned their lesson
or we're not getting through to the right person. 
Come on, Kelloggs. Let's talk. This has been fun.
This is a fun video to do and I don't think that's 
just the sugar speaking. So, thanks for watching.
I really appreciate that. Oh, I'm on tour again. 
Please come and see me on tour. It's all around
the UK. Sorry people in America. You have to 
console yourself with your fantastic cereals. Um,
we're doing the Reading Hexagon on the 4th of 
March. It's like over a kilo human worth of seats
and it's called the Hexagon. And I insisted that 
they book me in to do my show there. And it'd be
very embarrassing if we don't have enough people. 
So come along there. We're in Nottingham a couple
nights before. Um they got a big paraboid at the 
front of um the Nottingham Art Center. That's
a lot of fun. And we end in Manchester, Sulford, 
Manchester. So it's a huge amount of fun. The show
well me to do. I assume the audience also have a 
good time called Getting Trigy with it. All the
links are below. Last night, however, spoke about 
this live on stage at an evening of unnecessary
detail. That's my uh intimate nerdy variety night 
that I run with Steve Mold and Heleni and us and
our buddies talk about things in unnecessary level 
of detail. And I was on stage chatting about this,
just talking to the audience, getting their 
thoughts. Had a lot of fun. Thank you everyone
who comes along to Unnecessary Details. If you're 
anywhere near London, we have two more of them in
March and June. Uh it's not a big room though, 
so it sells out pretty quick, but uh it's a lot
of fun. Come along. Uh and that's it. Uh thanks 
for watching the show. I'll see you all see you
all on tour. Why should I eat more and um if you 
see me after the show, I'll sign your calculators.
It's a lot of fun. Or bring a box. I'll sign 
cereal boxes. Hey, you bring it. I'll sign it.
They just get worse every mouthful. It's 
so bad. Hey, you you want some? Anyone?
Cereal artificially flavored. Tony Glazo.