Deep math of the folded pizza slice

Clearly Gaussian Curvature is NOT the reason why we fold the pizza slice.
We fold it because that’s a way that works, and I’d suggest we humans learned that from trial and error, whenever we ate things that were thin and floppy, from well before we ever had a concept of mathematical theory.

Gaussian theory may help us explain, in an uneccessarily complex way, why our food flops.
But we can make lightweight, stiff structures quite intuitively, without ever knowing it.

Y’aint from around here, are ya?

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In engineering, we call it increasing the “second moment of area” otherwise known as the “area moment of inertia” or simply “the moment of inertia”. It is the same reason some beams flex excessively and others do not.

Doesn’t it apply as an approximation to explain why folding the pizza stiffens it in the desired direction? Obviously, you can’t stiffen the unbaked dough by folding it because it just stretches.

Deep mathS(!!!) would be for Chicago-style pizza, surely?

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Just for you Corrections, typos, grammar flubs and errors

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No, folding the pizza in either way shown does not change what is called the “intrinsic metric”. That is, if you draw a bunch of lines on the pizza and then make the fold, neither the angles between the lines nor their lengths change. The amazing thing about Gaussian curvature is that it only depends on the intrinsic metric, not the precise details of how the surface sits in 3-dimensional space.

Now, adding in factors from real life pizza, the derivation of the theorem is going to get some error terms. You’d actually have to go through it all to be sure, but I would think that the error terms would be 3rd order or higher. So unless you have a lot of toppings, the theorem should be close enough to true to make no practical difference.

I’d been reading/watching some tutorials on complex curved shapes in jewelry making and metalworking recently that seem somewhat related.

https://www.google.com/search?q=anticlastic+curvature+gaussian+jewelry&tbm=isch

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Noted. Also, sorry. :-/

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Actually, that assumption does hold for Little Caesars ™.

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People have weird definitions of ‘hamburger’ - with some claiming that the meat patty alone can be called a hamburger. For me the minimum requirements to fit the definition is to have 2 buns and a mince meat patty.

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1 bun normally does me, but I like the idea.

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Yeah… you know what I mean… 1 bun halved :stuck_out_tongue:

Then there’s this:

(do not watch if hungry or extremely full)

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This is high school pizza maths. Sure, you need 3 axes to describe the shape but does it include a void? Does it enclose a space, thereby rendering that space unusable by any other object on earth (except maybe insertion of more food/American Pie-style desecration)? Obviously no.

That’s why this is what you need to get your heads around: DIY pizza kebab. Order a thin & crispy from your local cheap & nasty chain pizza shop. The more generic and nasty the better. Get them to not cut it. Hammer punch the crust with your fist to render it malleable, roll up the entire pizza, hold in two hands and shove it in your face. Sensible toppings are flat toppings: you want all that goodness to stay on there when you roll it. This style has 2 unforeseen benefits: Oil drips out of the bottom as you eat (yeah… you’ll need a plate or the box for protection) and if you got it delivered and they messed up and cut it (which happens a lot… must be pizza-maker muscle memory) then they’re legally obligated to send you another one.

WRT to inelastic assumptions and a certain pizza brand, good point. As it happens, Little Caesar’s is for dinner here tonight (no accounting for kiddos’ tastes). Unfortunately, my attempts to verify the theorem’s application met with frustration, as each sector of pizza laminate steadfastly refuses to flop whether folded or not.

I think the buns are a relatively new innovation. If you look at recipes for “Hamburg steaks” and “Hamburger steaks” from the early 20th century up through the 1950s, buns aren’t mentioned.

Incidentally, the Stone-Tukey Theorem (aka “Ham Sandwich Theorem”) says that of you take a hamburger in your sense - a 2-part bun with a patty between them - you can simultaneously bisect all three parts with a single plane. This is true even if the patty is miles from the bun. The theorem fails for cheeseburgers.

BTW, another practical use I’ve I’ve found for this principle is stiffening a bit of paper for use as a fan on a hot day.

I dunno about the Antipodes, but back home in Perfidious Albion, kebab-meat is a popular pizza topping. So are chips (a ‘London Pizza’, apparently. The fact that I’ve only ever seen it sold in a small village west of Newcastle notwithstanding).

ETA: actually, being as you guys invented that goon-sack roulette game with the boxed ‘port’ & the clothes-dryer, I am more than prepared to be both intrigued and alarmed by what youse put on pizzas…

I’ve seen them do that here too - but only at kebab shops that sell pizza. The chips one I have never seen, but then a friend ordered a “pizza” in Tokyo and got corn on the cob and uncut steak on a piece of oven-baked lebanese bread, so I’d say the international benchmark for what constitutes a pizza is fairly low.

Just to clarify for all involved: the “goon-sack roulette game” is called Goon of Fortune - goon being a slang term for wine that comes in a box. You can get port too, but it’s usually just wine. You can apparently get decent wine in a box here and it is actually preferable to bottles in most circumstances: more environmentally friendly, the wine is not exposed to oxygen every time you pour a glass and when you finish the wine you can inflate the bag part for a makeshift pillow. Also, to avoid confusion, he’s talking about a “hill’s hoist” clothesline not a clothes-dryer, the insertion of wine into which could result in a house fire :smile:

We love goon so much here that we build monolithic monuments to it to please the gods.

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I assume you can get kangaroo pizza down under? Emu?

As far as boxed wine goes, I think it’s actually okay. Like screw-caps instead of corks, it’s actually a good idea, but does badly on the snob side of things.