
Gauss’s “Remarkable Theorem” and the best way to hold a pizza slice (2014) - amjd
https://aatishb.com/2014/09/05/curvature-and-strength/
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amjd
The same concept applies in the human foot in the form of three arches that
allow us to walk and run.

I recently read an article about the role of the tranverse arch on HN, but
can't find the link. Here are two others that talk about the same thing:

[https://www.nature.com/articles/d41586-020-00472-z](https://www.nature.com/articles/d41586-020-00472-z)

[https://www.nationalgeographic.com/science/2020/02/why-
human...](https://www.nationalgeographic.com/science/2020/02/why-human-feet-
evolved-arches-what-happens-if-you-lack-them/)

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burlesona
This was a surprisingly good and entertaining read, about much more than just
pizza slices. The title doesn’t do it justice, IMO :)

The example of the folded paper holding the can of beans really drove the
whole thing home for me.

~~~
dreamer7
Agreed. I almost skipped the article due to the start. I'm glad I didn't. Now
I'm seeing all the curved surfaces around me that were hiding in plain sight.

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bch
Allow Cliff Stoll to dine, educate and entertain you - [https://youtu.be/gi-
TBlh44gY](https://youtu.be/gi-TBlh44gY)

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skibz
I'm definitely going to ask somebody to "please pass the hyperbolic
paraboloids" the next time I have Pringles.

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ani-ani
" _To crack an egg open, you first need to dent it. When the egg loses its
curvature, it loses its strength._ "

I felt like this part could use some fleshing out. I'm pretty sure that the
egg does not lose its strength because it "loses its curvature", tough I must
admit I'd be hard pressed to provide a more precise explanation. I would say
it has more to do with the "hand wrap" spreading out the force over a wide
area, so that the egg's curvature causes the hand's force to work against
itself. But a small discontinuity creates a focus point where the force will
be localized, causing successively more breakage in the shell.

~~~
mcnamaratw
The article is accurate. A piece of paper can bend without tearing. An
eggshell can't. The difference is the shape.
[https://en.wikipedia.org/wiki/Gaussian_curvature](https://en.wikipedia.org/wiki/Gaussian_curvature)

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axaxs
What's with all the "I figured this out by myself..." comments? The article
says as much, that people figure this out themselves. It's just giving some
insight into why that works...

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mcnamaratw
I think the message is that we're all as smart as Gauss.

~~~
ninjinxo
This 19th century math genius taught us how to add the numbers from 1 to 100

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mcnamaratw
1 weird trick adds numbers from 1 to 100. Math teachers hate him!

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notRobot
Brilliant numberphile video on the topic: [https://www.youtube.com/watch?v=gi-
TBlh44gY](https://www.youtube.com/watch?v=gi-TBlh44gY)

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60654
By the way, this "best way" is so not true for deep dish pizza.

Good luck folding a slice of Giordano's! ;)

But on the plus side, it has its own structural integrity that makes folding
unnecessary :)

~~~
stephenr
That’s because what you’re calling pizza is in fact an eggless, tomato and
cheese quiche.

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AareyBaba
Jon Stewart's rant on deep dish pizza is a classic
[https://www.youtube.com/watch?v=cNYasqVmbiw](https://www.youtube.com/watch?v=cNYasqVmbiw)

~~~
stephenr
I love that clip

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regularfry
Incorrect. It is mathematically satisfying, but inefficient. The best way to
hold a pizza slice is with another one on top, sandwiching the topping, so you
get a double thickness with the base on the outside so you don't get tomato on
your hands.

~~~
stephenr
... why are your hands touching the top of the pizza?

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longtimegoogler
It doesn't always work in my experience. The problem is as you get near the
tip of the pizza sometimes it is too narrow to curve and since the line across
the pizza is now flat the front drops down.

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credit_guy
If anyone is curious, here's Gauss's book [1] that contains the theorem. It is
in Latin (Gauss published only in Latin), and you can find it at the bottom of
page 24.

And here's the English translation [2]. The theorem is on page 20.

[1]
[https://books.google.com/books?id=bX0AAAAAMAAJ](https://books.google.com/books?id=bX0AAAAAMAAJ)

[2]
[https://books.google.com/books?id=a1wTJR3kHwUC](https://books.google.com/books?id=a1wTJR3kHwUC)

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ubasu
It's not about curvature, it's moment of inertia that stops it from bending,
see:

[https://news.ycombinator.com/item?id=8275112](https://news.ycombinator.com/item?id=8275112)

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kiliantics
a friend helped create this video on the same topic:

[https://www.youtube.com/watch?v=HGl3_92KW7I](https://www.youtube.com/watch?v=HGl3_92KW7I)

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CPLX
As a 20th century genius from Brooklyn I managed to figure this out
independently while drunk and on the way to the subway.

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gotoeleven
That may be how a math genius holds their pizza, but a Real Stable Genius
holds it backwards and eats the crust first.

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vlod
Meh this is obvious. In NY, if you DON'T do this, you get the Niagara Falls of
pizza-goop straight onto your lap.

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thaumasiotes
> The iconic shape for a nuclear power plant cooling tower also incorporates
> curvature in both directions. This shape, called a hyperboloid, minimizes
> the amount of material required to build it.

What? This is completely meaningless. A hyperboloid shape minimizes the amount
of material required _to match what constraints?_ If the goal is to minimize
the amount of material while reaching a certain height, you just want a pole.
If the goal is to minimize material, full stop, just don't build the tower in
the first place. What's the goal supposed to be?

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labawi
They presumably have a set of complex constraints on cooling towers. A
hyperboloid fullfills them with less material than a cylinder.

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hmd_imputer
hmm, I don't think you need to be a math genius to develop an intuitive
feeling for it.

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ComputerGuru
No, not at all. But to provide a mathematical basis and proof that can then be
extended to all walks of life?

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weeksie
In New York we just fold 'em in half.

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DonHopkins
That's how the Pizza Rats carry them so far without losing all the toppings.

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fit2rule
I always fold and make it a pie in the hand. Better than cheese in the bush.
;)

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Asooka
I just use a knife and fork. Like a normal person.

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Jailbird
That is decidedly abnormal in the NYC area. Eat as you wish, but you may find
it more enjoyable our way!

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collyw
If I worked this out by myself, can I be considered a mathematical genius?

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mrkramer
I figured this out long time ago. Bending a pizza slice helps because top of
the pizza slice doesn't fall down.

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dntbnmpls
Maybe for the first bite or two, but the best way hold a slice is to fold it
almost in half or completely in half ( depending on your preference ) and
eating it that way. This way you get the full width of the pizza in one bite.
Only children and tourists hold pizza as shown in the article. Don't have a
fancy formula for it, just a lifetime's experience of eating pizza slices.

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ComputerGuru
You mean, taking the math and science described in intricate detail in this
article to the next level, right?

I fail to see how what you’re saying negates the article. In fact, there are
several descriptions of folding as being the next step (see folded paper
holding a can of beans).

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dntbnmpls
I just looked at the pictures.

What they recommended.

[https://aatishb.com/images/2014/08/pizza-fold-
hold.png](https://aatishb.com/images/2014/08/pizza-fold-hold.png)

vs

What I do.

[https://assets.bonappetit.com/photos/5a9dd665eb730726d6c7ec1...](https://assets.bonappetit.com/photos/5a9dd665eb730726d6c7ec14/master/w_1600%2Cc_limit/pizza-
slice-full-fold.jpg)

If the article said to fold it in half, then we are in agreement. But the
picture they provided didn't show that.

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shawnz
The article says to apply a curvature opposite to the direction it sags in.
Whether it's a full 180 degrees or not doesn't matter, you get the effect with
any amount of curvature.

Actually, if you fold it totally flat then presumably you'd lose the curvature
and it would sag again, so that seems unoptimal to me. Plus, how could you
taste the toppings?

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jamessb
> Plus, how could you taste the toppings?

How do you taste the filling in a sandwich?

~~~
shawnz
Fair point.

