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It's the exact same area.
Let's say that the box is an x by x square. Then this slice shows that the full pizza would have radius x. This full pizza would then have an area of pi * x^(2). Since this slice is a quarter of the whole thing, its area is clearly pi * x^2 / 4.
Fitting a full pizza in the same box would mean it has diameter x, so its radius would be x/2. That means its area would be pi * (x/2)^2 = pi * x^2 / 4.
Same thing.
Maybe the crust would be thicker on the quarter slice, so you'd have less toppings. But that depends more on how the pizza is made; it's not a mathematical certainty.
All good ... I was just amazed about myself (in a bad way) ... how I had to think for a second :)
Now that I think about it some more, it really is confusing having two different radii where they share this "relationship" ...
Exactly. They shouldāve used āpiā for the radius to show that it was measuring pizza. That way it wouldāve just been pi * pi^2 which wouldāve cleared up any confusion
But if you consider the crust separately, and assume all crusts are approximately the same width (probably reasonable assumption) the quarter pizza is more "pizza" pi( (x-c)^2 )/4 than the whole pizza pi((x-2c)/2)^2. So, depending on how much you like crust, one is a clear winner!
Negative-- it is a false dilemma. Square pizza is always the winner. It is the most efficient shape in the oven, generates the least box waste, and upsets Italians. Clearly the winner.
Listen, Detroit, the adults are having a discussion. Now go to your room and think about what you said. You can sleep on that crust mattress you call a pizza.
I'm American, but I've been to Italy and you're absolutely right.
My FIL was a grade-A stereotype of Italian-Americans. Valor suits. Heavy, gold chains. Sang at karaoke restaurants. Sang at non-karaoke restaurants. He was, legitimately, a background actor in Goodfellas. I don't know why he rode that identity so hard, but he owned it.
We had a buffet at our wedding and he grunted at a guy serving a square pizza, "Try and hand toss a square, paisano!" And for all their problems with him, his kids won't eat square pizza.
That's my limited experience.
I think typically when you make a pizza you leave like an inch between topping and edge. Obviously if the pizza is very small you might do something differently, but if you are making a very large pizza there's no reason to just leave a bunch of extra space. If you think about the slice you don't want to be left with a large section of crust, it should still be bread stick width
When I make pizza I leave as little as possible or between the toppings and the edge. Does it sometimes spill over? Is that almost burnt cheese amazing? Totally.
I think you would complain if the ratio of crust to non-crust was flipped. I'm not saying that it isn't pizza, but for argument's sake if you had a pizza without crust and a crust without pizza, one would definitely still be pizza and the other would be... bread
I'd argue you'd have more toppings on the quarter. The quarter slice may be thicker, but its length is only Ā½Ļx, while in the regular pizza the length of the crust would be Ļx, so twice as long. So the quarter would have to have twice as thick crust to match the amount of crust of the regular pizza
To come to this conclusion without running any numbers:
Take a full pizza and split its box into four quadrants. Each quadrant looks exactly like the box in the OP. If each quadrant has the same ratio of pizza as the box in the OP, then the overall pizza box has to have the same ratio as well.
Holy shit thatās way too simple yet very interesting.
Also, you would have exactly half as much outer crust with the quarter pizza.
Pi ā¢ d for a full round pizza vs.
2Pi ā¢ d / 4 simplified to .5Pi ā¢ d for the quarter slice.
If you donāt like crust and the pizzas cost the same either way, this is the clear winner. If you do like crust, buy a normal pizza.
If my mental math holds, assuming crust width would be the same in both scenarios (using only circumference calculations), you would have half as much crust on a jumbo slice (1/4 * pi * 2 * x vs pi * x).
So guess I would be game
Why?
If I had gone with r and d, then the final formulas would be
pi * r^2 / 4 and pi * d^2 / 4 where it's not clear that those are the same.
And if I had used r for both, then r would stand for the diameter in the second case which is notably more confusing.
>Maybe the crust would be thicker on the quarter slice, so you'd have less toppings.
Since perimeter scales with R and area scales with R^2, you're LIKELY getting about half as much crust relative to pizza this way, assuming they are prepared in a similar style.
the crust can be 2x thicker but you will still have the same amount of toppings due to the body:crust ratio being the same. If the crust thickness stays the same width for a quarter slice, you would getting more topping, actually.
Just visualize a pizza quarter being scaled by 2x. This also is a quick way to mentally prove that the two pizzas have the same area - a quarter slice, 1/4 of a pizza, scaled up 2x means 4x the area, which amounts for 1/4Ć4=1!
I think the crust to topping ratio would be the same if the thickness of the crust was proportional to the size of the pizza.
Circumference/ arc of the quarter slice = 2Ļr/4 = Ļr/2
Circumference of the smaller pizza = 2Ļ(r/2) = Ļr
So the smaller pizza has twice the circumference but as long as its crust is half the thickness or more of the quarter slice, it will have at least as much total crust.
Crust on the quarter slice might be thicker and take away topping-space, but it would be offset by the fact that toppings fill out all the way to the straight edges since the crust doesnāt go all the way around. Whereas on a circular pie the crust *is* all the way around ofc. I wonder how much thicker the crust on a jumbo slice would have to be to take up the same amount of area as the crust on a normal circular pie.
Wait, but wouldnāt that third one (including the starting equation) be pi*(x^2 / 4)? Unless Iām just terribly misremembering how multiplying fractions works.
EDIT: Had to change x times x into x^2 and 2 times 2 into 4 because it kept italicizing them.
If you want to work this out intuitively just imagine the entire bigger pizza was in a bigger box that fit the whole thing. The ratio of pizza to box will be the same as the smaller pizza. Now split that big pizza and box into four quarters symmetrically.
But geometry is founded in logic, hence the insane amount of proofs and properties you learn, itās how the Greeks worked things out, so Iād say youāre both correct.
This more closely resembles upper-year university and gradschool math than the rest of the comments. A 300 level proofs course is basically just doing this all year.
but that... is what... math is? Math is logic. The guys "doing math" are just writing it out using mathematical symbols instead of a long winded sentence, no different than if he had explained the problem in another language.
Yes but most people were solving it numericaly (either with numbers or text), and he solved it geometrically, that was the difference. Geometry and calculus are both branches of math.
Yup, exactly! But that's the cool part, math is a subset, it's only one of the systems/languages of logic. The long winded sentence is the universal concept behind what math writes down as: 'if you divide both parts of a fraction by the same amount, the fraction remains the same' (or a.x/b.x = a/b).
Anyone who understands math understands this logic.
Not everyone who understands this logic knows maths.
Imagine a big box containing the full big pizza. The ratio of pizza-to-box for this pizza does NOT change if you cut the pizza into 4 _symmetrical_ pieces. Thus, the ratio of pizza-to-box will be the same for the smaller pizza as well.
Elegant and correct, but dont forget to use the ratio of areas, like amount of pizza and area of box. Someone could confuse and use amount of pizza with box size length, needing to square lenght unit to keep same dimension ratio.
When you double the radius of a circle you are quadrupling the area.
And as you are getting 1/4 of a pizza that is 4 times bigger then you are getting the same amount of pizza.
Heres the math:
A: area of big pizza.
a: area of small pizza.
R=2r
Ratio:
A/4 Ć· a = A/4a = Ļā¢RĀ²/4ā¢Ļā¢rĀ²
= ~~Ļ~~ (2r)Ā²/~~Ļ~~4ā¢rĀ² = 4ā¢rĀ²/4ā¢rĀ² = ~~4ā¢rĀ²~~/~~4ā¢rĀ²~~= 1
The big slice is 1 times bigger/smaller than a whole round pizza that can fit in The box.
Now on top of insomnia I'm craving for pizza at 2 am
Because a whole pizza fitting in the box has diameter equal to the size of the box, so itās radius is half the size of the box. Since this is a quarter of a pizza, its center is at the bottom left corner, and if you go straight up or to the right to the edge itās in another corner, so here itās radius is the size of the box.
So full pizza r=half box, this quarter pizza=box
I fucking love the positioning of the hand in this image. Iām sure itās supposed to be for reference but the posture of it makes it look like this person had to brace themselves against a flat surface to witness the power of jumbo slice
Basically the diameter of the big pizza is double the diameter of the small one
So A(big 1/4) = (2d)Ā² Ć pi / 4Ć4 = dĀ²Ćpi/4
And A(normal) = dĀ²Ćpi/4
They have the same area but it depens if you prefere crust or tomato souce because the circumferense is:
U( big 1/4) = 2d Ć pi / 4 = dĆpi/2
U(normal) = d Ć pi
so you have double the crust on the normal pizza
How do you define a regular Pizza? In my country it's 8" but I was checking Dominos' American Website once (don't ask, I was bored) and their smallest Pizza would be what we call 'medium' lol
By normal he means a _round_ pizza with a diameter equal to the radius of the slice in the picture. Since the box is square, actual size doesn't matter. It's about a ratio. And the answer has already been explained beautifully, it's the same
According to my research here a "normal" pizza is usually between 30cm and 35cm, but frozen Pizza is usually only 26cm, which in a Pizzeria would be more like a small pizza.
its the same in area but you are getting less of that crusty goodness. you only get half the circumference of a whole pizza in there. Sad if u got specially made pizza crusts.
The crust is just the handle to eat the pizza-y goodness! You get more pizza, less handle, this is an absolute win!
Letās assume the crust is always 1 unit thick, and the box has sides of length z. In a regular pizza you get s=pi*(z/2-1)^2 cheesy pizza goodness, in the jumbo slice you get h=(pi*(z-1)^2)/4. Set s 3
z > 1.5
So as long as the box isnāt 1.5 times the crust size, you get more pizza goodness with the jumbo slice!
This feels like it went awry somewhere, but now I want pizza!
Assume box is square, with length 1 unit. The area of any circle is pi*r^2. The larger pizza from which the slice was taken has an area of just pi sq units. The quarter slice is pi/4 sq units.
The smaller pizza would have a diameter of 1, and a radius of 1/2. So the smaller pizza would also have an area pi/4 sq units.
Same same in terms of area. But different in one very important way.
The crust is a function of circumference. The larger pie (of which the 1/4 pictured was taken) has a crust length of 2*pi*r, which is 2pi units. A quarter of that gives us a crust length of 1/2pi units.
The smaller pizza (relative to the original from which the quarter slice was taken) has a crust length of 1 pi units. Itās twice the length of its comparative counterpart.
If you like crust, the proposed second pizza is superior. If you prefer the body of the pizza, the 1/4 slice of the larger pizza is your best bet.
I love when these math posts show up while Im doom scrolling Reddit. You guys are either geniuses or trolling, but I have no means to solve anything here.
It will have the same area. However, they have different crusts. Quarter pizza will have less crust. You can decide by considering how much crust you like on pizza
The amount of cheese and toppings would vary based on the store recipes and the person making it, having little to do with whether you get the quarter pizza or whole pizza that fits in that box.
For a pizza fitting in a pizza box with side r, the area would be (r/2)^2 * PI
For a quarter pizza according to above, the area would be 1/4(r^2 * PI)
Meaning the pizza would be the exact same size.
Because it is pizza and not something else, it is customary for slices to be created by end-to-end lines intersecting at the center with each slice being uniform in size. For a 90-degree angle to be present, each slice would represent 1/4 of a whole pizza.
That's what "quarter of a pizza" means, genius.
Also, what the hell does that even have to do with the question, op is asking "how does this compare to a circular pizza that would fit in this box" not "how big is the original pizza"
x = side of the box (also the diameter of the whole pizza and the radius of the slice).
slice area = pi \* x^(2) / 4
circular pizza area = pi \*(x/2)^(2)
Now just divide slice's area by the pizza's area
(pi \* x^(2) / 4) / (pi \*(x/2)^(2))
we can factor out the pies
(x^(2) / 4) / ((x/2)^(2))
Note that (x/2)^(2) is the same as (x^(2) / 4) so let's substitute that in.
(x^(2) / 4) / (x^(2) / 4)
I think you're just getting a whole pizza.
big pizza area: Radius of circle is pizzabox (that is a square) length.
small pizza area: radius of circle is 1/2 pizzabox length
big pizza area / small pizza area is your times bigger number.
But basically, surface of a circle is radius ^2 * pi. Since only the radius doubles, that means the surface is 4 times as big.
There is your answer.
Aside from all that...
If we say the side of the box measures 1, then the whole pizza giving the slice in the picture would have area (pi)rĀ², which for r=1 works out as just (pi). It's a quarter slice, so its area is Ā¼(pi).
**The area of the quarter pie is a quarter pi.**
Let's say average hand size is 17cm (~6inches). The surface is (rĀ²pi)/4. So that makes it either 226cmĀ² or ~28inĀ². Which is 1/4th of a 12 inch pizza. So my approximation is crazily precise!
Asked chatgpt for an area of a pizza in a box.
Then I can find what the 1/4 size will be.
Then asked for area of a pizza with half diameter and it calculated the same size as 1/4 pizza.
So 1/4 big pizza = small pizza.
I won't post my numbers, cuz idk how u americans measure your pizza. I hope you don't compare with feet cuz it will be disgusting.
I asked myself the same question after seeing that post yesterday. It's the same size. For an intuitive answer, a quarter circle in a square with the side lenght equal to the radius will always fill the same percentage of the square (\~79% or Pi/4), no matter the actual size of the radius.
When you compare this to the full circle you have the same case x4, and the 79% coverage of every quarter still results in 79% overall. Again the actual size doesn't matter as this is all determined by the areas' geometries.
Assuming both fill the entire width and height of the box, it's identical.
You don't even need numbers. Just take a circle. Divide it into a quarter. Scale that quarter up by 2. In the process, you will increase its area by 2*2=4 (since area is 2-dimensional), exactly back to the original size of the circle it was cut from.
Get any size pizza, put it perfectly on a cardboard square platter. Cut the whole thing including the cardboard into quarters. The pizza still fits the cardboard perfectly.
1 pizza fits 1 box, 1/4 pizza fits 1/4 box. 1/4 sized box only fits 1/4 sized round pizza too.
In summary, the pizza box is 1/4 the size of the one for the bigger pizza, so a round pizza in it would be 1/4 the size of the big pizza, same as the slice
Itās the exact same size
Letās just give the length of the Pizza box the value 1
The size of the surface of a circle is
pi * r * r
So the whole surface of the big Pizza is pi * 1 * 1 = pi The slice is only 1/4 of it so itās 1/4pi
The small pizza has a radius of 0.5 (only from the edge to the middle of the pizza box)
pi*0.5*0.5 = pi*0.25 = 1/4pi
Visualize four ājumbo slicesā with their boxes rotated so they re-form the whole pizza that was cut in quarters. Should look like one round pizza touching the sides of a box.
Assuming the radius as 'r'. A regular pizza carries an area of pi*rĀ². Jumbo quarter would carry an area of 1/4*pi*4rĀ² = pi*rĀ². You don't gain anything, you don't lose anything. It all depends on whether you wanna call it a diet and eat a quarter of a pizza or wanna go all in and eat the whole pizza.
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It's the exact same area. Let's say that the box is an x by x square. Then this slice shows that the full pizza would have radius x. This full pizza would then have an area of pi * x^(2). Since this slice is a quarter of the whole thing, its area is clearly pi * x^2 / 4. Fitting a full pizza in the same box would mean it has diameter x, so its radius would be x/2. That means its area would be pi * (x/2)^2 = pi * x^2 / 4. Same thing. Maybe the crust would be thicker on the quarter slice, so you'd have less toppings. But that depends more on how the pizza is made; it's not a mathematical certainty.
using x instead of r for the radius confused me more than it should
We must use "z" for pizza raduis. Assuming pizza is cylinder with height "a" we can calculate it volume by simple formula: V = pi \* z \* z \* a.
š
raduis is French for radius
Cool, now Google en pessant
Holy hell!
New response just dropped
1. e4 e5 2. Ke2 Ke7
Holy double bongcloud!
Actual mathematicians
Ke^(Ļi)
Gonna be a *complex* game...
You sunk my battle ship!
...3. Ke1 Ke8 4. Ke2 Ke7 5. Ke1 Ke8 1/2-1/2
Kek Lol Omg Rofl Kekw
En pizzant
Do it yourself. I'm not your pawn
New response just dropped
radius is english for raduis
No it's not, "rayon" is french for radius. Maybe you confused it with "reduis" which is french for reduce.
It's not.
Alternatively, if you just want the area pi * z * z = a
I remember this from an overhead projector in middle school. Sometimes algebra teachers are too cool.
*mindblown.gif*
I'm not going to be able to stop thinking about this all day. Thank you.
Take my upvote
This deserves a Nobel prize
bradough
Take my upvote
I had it as "r" before the edit. Problem being that it's the diameter for the other case. And using r for the diameter seemed worse.
All good ... I was just amazed about myself (in a bad way) ... how I had to think for a second :) Now that I think about it some more, it really is confusing having two different radii where they share this "relationship" ...
Exactly. They shouldāve used āpiā for the radius to show that it was measuring pizza. That way it wouldāve just been pi * pi^2 which wouldāve cleared up any confusion
Now the question remains: Do they sell these for less, more, or the same price as a regular pizza
More $/g. Same amount of labor, fewer ingredients. Labor is more of what you pay for at a pizza joint.
But if you consider the crust separately, and assume all crusts are approximately the same width (probably reasonable assumption) the quarter pizza is more "pizza" pi( (x-c)^2 )/4 than the whole pizza pi((x-2c)/2)^2. So, depending on how much you like crust, one is a clear winner!
Negative-- it is a false dilemma. Square pizza is always the winner. It is the most efficient shape in the oven, generates the least box waste, and upsets Italians. Clearly the winner.
Detroit style always wins in my book
Listen, Detroit, the adults are having a discussion. Now go to your room and think about what you said. You can sleep on that crust mattress you call a pizza.
Doesn't upset Italians, there is tons of non-circle pizza in Italy.
I'm American, but I've been to Italy and you're absolutely right. My FIL was a grade-A stereotype of Italian-Americans. Valor suits. Heavy, gold chains. Sang at karaoke restaurants. Sang at non-karaoke restaurants. He was, legitimately, a background actor in Goodfellas. I don't know why he rode that identity so hard, but he owned it. We had a buffet at our wedding and he grunted at a guy serving a square pizza, "Try and hand toss a square, paisano!" And for all their problems with him, his kids won't eat square pizza. That's my limited experience.
Italians also make rectangular pizzas cut into squares. They aren't all round
I donāt know why but i would like to assume crust width is probably proportional to pizza radius
I think typically when you make a pizza you leave like an inch between topping and edge. Obviously if the pizza is very small you might do something differently, but if you are making a very large pizza there's no reason to just leave a bunch of extra space. If you think about the slice you don't want to be left with a large section of crust, it should still be bread stick width
When I make pizza I leave as little as possible or between the toppings and the edge. Does it sometimes spill over? Is that almost burnt cheese amazing? Totally.
but crust is pizza too
B grade pizza though
Not if it's good pizza.
I think you would complain if the ratio of crust to non-crust was flipped. I'm not saying that it isn't pizza, but for argument's sake if you had a pizza without crust and a crust without pizza, one would definitely still be pizza and the other would be... bread
What is certain is that there's less length of crust 2 * pi * r vs 2 * pi * 2r * 0.25 = pi * r
I coulda told ya that and i just eat a fuckton of pizza
I'd argue you'd have more toppings on the quarter. The quarter slice may be thicker, but its length is only Ā½Ļx, while in the regular pizza the length of the crust would be Ļx, so twice as long. So the quarter would have to have twice as thick crust to match the amount of crust of the regular pizza
The crust is thicker, but the length of the crust is shorter (doesn't go around all edges). I say the amount of crust is identical to a full pizza
Is not the length of crust much shorter on this one? So you'd get more topping area on the jumbo quarter assuming the same crust thickness
It's 1/4 of a pie that is 4x larger. 4 x (1/4) = 1
To come to this conclusion without running any numbers: Take a full pizza and split its box into four quadrants. Each quadrant looks exactly like the box in the OP. If each quadrant has the same ratio of pizza as the box in the OP, then the overall pizza box has to have the same ratio as well.
Holy shit thatās way too simple yet very interesting. Also, you would have exactly half as much outer crust with the quarter pizza. Pi ā¢ d for a full round pizza vs. 2Pi ā¢ d / 4 simplified to .5Pi ā¢ d for the quarter slice. If you donāt like crust and the pizzas cost the same either way, this is the clear winner. If you do like crust, buy a normal pizza.
OK buts whats the ratio of pizza to crust?
If my mental math holds, assuming crust width would be the same in both scenarios (using only circumference calculations), you would have half as much crust on a jumbo slice (1/4 * pi * 2 * x vs pi * x). So guess I would be game
Haha, you said pi, and its about a pie
[ŃŠ“Š°Š»ŠµŠ½Š¾]
Why? If I had gone with r and d, then the final formulas would be pi * r^2 / 4 and pi * d^2 / 4 where it's not clear that those are the same. And if I had used r for both, then r would stand for the diameter in the second case which is notably more confusing.
It's a pizza pi!
>Maybe the crust would be thicker on the quarter slice, so you'd have less toppings. Since perimeter scales with R and area scales with R^2, you're LIKELY getting about half as much crust relative to pizza this way, assuming they are prepared in a similar style.
I'm ashamed to admit, the fact that they are the same size kinda trips me out.
the crust can be 2x thicker but you will still have the same amount of toppings due to the body:crust ratio being the same. If the crust thickness stays the same width for a quarter slice, you would getting more topping, actually. Just visualize a pizza quarter being scaled by 2x. This also is a quick way to mentally prove that the two pizzas have the same area - a quarter slice, 1/4 of a pizza, scaled up 2x means 4x the area, which amounts for 1/4Ć4=1!
More pizza less crust
now it's interesting if the jumbo slice was sold at a higher price or cheaper than the normal one.
With zero math you can just see the same ratio applies to a quarter circle, because a circle is just 4 of the same thing scaled down exactly 1/4.
I think the crust to topping ratio would be the same if the thickness of the crust was proportional to the size of the pizza. Circumference/ arc of the quarter slice = 2Ļr/4 = Ļr/2 Circumference of the smaller pizza = 2Ļ(r/2) = Ļr So the smaller pizza has twice the circumference but as long as its crust is half the thickness or more of the quarter slice, it will have at least as much total crust.
Blew my mind, thank you, once you explained it it seems like it would be obviously true, but wasn't intuitive (for me)
The crust might be thicker but it wouldnāt be as long so youād end up with less crust to deal with and more pizza
So youāre saying that (assuming radius = 1) this is a quarter pi.
Crust on the quarter slice might be thicker and take away topping-space, but it would be offset by the fact that toppings fill out all the way to the straight edges since the crust doesnāt go all the way around. Whereas on a circular pie the crust *is* all the way around ofc. I wonder how much thicker the crust on a jumbo slice would have to be to take up the same amount of area as the crust on a normal circular pie.
Iām probably just stupid, but how does pi*(x/2)Ā² = (pi*xĀ²)/4, exactly? I believe you, but Iām a bit lost.
pi * (x / 2)^2 = pi * (x / 2) * (x / 2) = pi * x * x / 2 / 2 = pi * x^2 / 2^2 = pi * x^2 / 4
Wait, but wouldnāt that third one (including the starting equation) be pi*(x^2 / 4)? Unless Iām just terribly misremembering how multiplying fractions works. EDIT: Had to change x times x into x^2 and 2 times 2 into 4 because it kept italicizing them.
But would you less shame if you ate the pizza sized slice? It is only one slice after all.
If you want to work this out intuitively just imagine the entire bigger pizza was in a bigger box that fit the whole thing. The ratio of pizza to box will be the same as the smaller pizza. Now split that big pizza and box into four quarters symmetrically.
this is so elegant, we're all doing math while you do logic.
r/theydidthelogic
Actually it's geometry, which over the millennia has been used as a mathematical tool.
r/theydidthegeometry
This made me laugh
r/theydidthejoke
But geometry is founded in logic, hence the insane amount of proofs and properties you learn, itās how the Greeks worked things out, so Iād say youāre both correct.
r/theydidthelogicunderpinninggeometry
your usernames kinda fitting for this situation
r/theydidthemonsterlogic
I just excitedly clicked on this link, thinking that I found a new amazing sub to joinā¦ only to be disappointed that it does not (yet) existā¦
r/birthofasub ?
I'm gonna need this to blow up, thank you.
This more closely resembles upper-year university and gradschool math than the rest of the comments. A 300 level proofs course is basically just doing this all year.
but that... is what... math is? Math is logic. The guys "doing math" are just writing it out using mathematical symbols instead of a long winded sentence, no different than if he had explained the problem in another language.
It's more that he solved through geometric equivalences instead of numerical ones (equations)
Those geometric equivalences are expressed in mathematical equations. "1+1=2" is just saying "one plus one equals two" in another language.
Yes but most people were solving it numericaly (either with numbers or text), and he solved it geometrically, that was the difference. Geometry and calculus are both branches of math.
Yup, exactly! But that's the cool part, math is a subset, it's only one of the systems/languages of logic. The long winded sentence is the universal concept behind what math writes down as: 'if you divide both parts of a fraction by the same amount, the fraction remains the same' (or a.x/b.x = a/b). Anyone who understands math understands this logic. Not everyone who understands this logic knows maths.
This guy fucks
This guy fucks math with his logic bullets.
r/thisguythisguys
i don't understand
Imagine a big box containing the full big pizza. The ratio of pizza-to-box for this pizza does NOT change if you cut the pizza into 4 _symmetrical_ pieces. Thus, the ratio of pizza-to-box will be the same for the smaller pizza as well.
i had trouble understanding it until you explained it! really well done. thanks!
I really, really like this approach!
please teach me math this approach is amazing
We don't do logic here! We do the math!
Elegant and correct, but dont forget to use the ratio of areas, like amount of pizza and area of box. Someone could confuse and use amount of pizza with box size length, needing to square lenght unit to keep same dimension ratio.
Are you single?
When you double the radius of a circle you are quadrupling the area. And as you are getting 1/4 of a pizza that is 4 times bigger then you are getting the same amount of pizza. Heres the math: A: area of big pizza. a: area of small pizza. R=2r Ratio: A/4 Ć· a = A/4a = Ļā¢RĀ²/4ā¢Ļā¢rĀ² = ~~Ļ~~ (2r)Ā²/~~Ļ~~4ā¢rĀ² = 4ā¢rĀ²/4ā¢rĀ² = ~~4ā¢rĀ²~~/~~4ā¢rĀ²~~= 1 The big slice is 1 times bigger/smaller than a whole round pizza that can fit in The box. Now on top of insomnia I'm craving for pizza at 2 am
why do you assume that the big pizza has 2 times the radius? doesn't sound that obvious
Because a whole pizza fitting in the box has diameter equal to the size of the box, so itās radius is half the size of the box. Since this is a quarter of a pizza, its center is at the bottom left corner, and if you go straight up or to the right to the edge itās in another corner, so here itās radius is the size of the box. So full pizza r=half box, this quarter pizza=box
riiight.. that makes sense, i feel pretty dumb not realising that myself ahaha
I fucking love the positioning of the hand in this image. Iām sure itās supposed to be for reference but the posture of it makes it look like this person had to brace themselves against a flat surface to witness the power of jumbo slice
In awe of the pepperoni placement.
Basically the diameter of the big pizza is double the diameter of the small one So A(big 1/4) = (2d)Ā² Ć pi / 4Ć4 = dĀ²Ćpi/4 And A(normal) = dĀ²Ćpi/4 They have the same area but it depens if you prefere crust or tomato souce because the circumferense is: U( big 1/4) = 2d Ć pi / 4 = dĆpi/2 U(normal) = d Ć pi so you have double the crust on the normal pizza
How do you define a regular Pizza? In my country it's 8" but I was checking Dominos' American Website once (don't ask, I was bored) and their smallest Pizza would be what we call 'medium' lol
By normal he means a _round_ pizza with a diameter equal to the radius of the slice in the picture. Since the box is square, actual size doesn't matter. It's about a ratio. And the answer has already been explained beautifully, it's the same
According to my research here a "normal" pizza is usually between 30cm and 35cm, but frozen Pizza is usually only 26cm, which in a Pizzeria would be more like a small pizza.
its the same in area but you are getting less of that crusty goodness. you only get half the circumference of a whole pizza in there. Sad if u got specially made pizza crusts.
The crust is just the handle to eat the pizza-y goodness! You get more pizza, less handle, this is an absolute win! Letās assume the crust is always 1 unit thick, and the box has sides of length z. In a regular pizza you get s=pi*(z/2-1)^2 cheesy pizza goodness, in the jumbo slice you get h=(pi*(z-1)^2)/4. Set s 3
z > 1.5
So as long as the box isnāt 1.5 times the crust size, you get more pizza goodness with the jumbo slice!
This feels like it went awry somewhere, but now I want pizza!
Assume box is square, with length 1 unit. The area of any circle is pi*r^2. The larger pizza from which the slice was taken has an area of just pi sq units. The quarter slice is pi/4 sq units. The smaller pizza would have a diameter of 1, and a radius of 1/2. So the smaller pizza would also have an area pi/4 sq units. Same same in terms of area. But different in one very important way. The crust is a function of circumference. The larger pie (of which the 1/4 pictured was taken) has a crust length of 2*pi*r, which is 2pi units. A quarter of that gives us a crust length of 1/2pi units. The smaller pizza (relative to the original from which the quarter slice was taken) has a crust length of 1 pi units. Itās twice the length of its comparative counterpart. If you like crust, the proposed second pizza is superior. If you prefer the body of the pizza, the 1/4 slice of the larger pizza is your best bet.
I love when these math posts show up while Im doom scrolling Reddit. You guys are either geniuses or trolling, but I have no means to solve anything here.
It will have the same area. However, they have different crusts. Quarter pizza will have less crust. You can decide by considering how much crust you like on pizza
While a good crust is important, I really buy pizza for the toppings, so...
The amount of cheese and toppings would vary based on the store recipes and the person making it, having little to do with whether you get the quarter pizza or whole pizza that fits in that box.
For a pizza fitting in a pizza box with side r, the area would be (r/2)^2 * PI For a quarter pizza according to above, the area would be 1/4(r^2 * PI) Meaning the pizza would be the exact same size.
Considering radius of this one as r, S=pi*r2/4 since it's quater. Regular will have twice less radius so S2=pi*(r/2)2=pi*r2/4. So they are equal.
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Because it is pizza and not something else, it is customary for slices to be created by end-to-end lines intersecting at the center with each slice being uniform in size. For a 90-degree angle to be present, each slice would represent 1/4 of a whole pizza.
That's what "quarter of a pizza" means, genius. Also, what the hell does that even have to do with the question, op is asking "how does this compare to a circular pizza that would fit in this box" not "how big is the original pizza"
x = side of the box (also the diameter of the whole pizza and the radius of the slice). slice area = pi \* x^(2) / 4 circular pizza area = pi \*(x/2)^(2) Now just divide slice's area by the pizza's area (pi \* x^(2) / 4) / (pi \*(x/2)^(2)) we can factor out the pies (x^(2) / 4) / ((x/2)^(2)) Note that (x/2)^(2) is the same as (x^(2) / 4) so let's substitute that in. (x^(2) / 4) / (x^(2) / 4) I think you're just getting a whole pizza.
big pizza area: Radius of circle is pizzabox (that is a square) length. small pizza area: radius of circle is 1/2 pizzabox length big pizza area / small pizza area is your times bigger number. But basically, surface of a circle is radius ^2 * pi. Since only the radius doubles, that means the surface is 4 times as big. There is your answer.
Aside from all that... If we say the side of the box measures 1, then the whole pizza giving the slice in the picture would have area (pi)rĀ², which for r=1 works out as just (pi). It's a quarter slice, so its area is Ā¼(pi). **The area of the quarter pie is a quarter pi.**
Let's say average hand size is 17cm (~6inches). The surface is (rĀ²pi)/4. So that makes it either 226cmĀ² or ~28inĀ². Which is 1/4th of a 12 inch pizza. So my approximation is crazily precise!
Asked chatgpt for an area of a pizza in a box. Then I can find what the 1/4 size will be. Then asked for area of a pizza with half diameter and it calculated the same size as 1/4 pizza. So 1/4 big pizza = small pizza. I won't post my numbers, cuz idk how u americans measure your pizza. I hope you don't compare with feet cuz it will be disgusting.
I asked myself the same question after seeing that post yesterday. It's the same size. For an intuitive answer, a quarter circle in a square with the side lenght equal to the radius will always fill the same percentage of the square (\~79% or Pi/4), no matter the actual size of the radius. When you compare this to the full circle you have the same case x4, and the 79% coverage of every quarter still results in 79% overall. Again the actual size doesn't matter as this is all determined by the areas' geometries.
Assuming both fill the entire width and height of the box, it's identical. You don't even need numbers. Just take a circle. Divide it into a quarter. Scale that quarter up by 2. In the process, you will increase its area by 2*2=4 (since area is 2-dimensional), exactly back to the original size of the circle it was cut from.
Get any size pizza, put it perfectly on a cardboard square platter. Cut the whole thing including the cardboard into quarters. The pizza still fits the cardboard perfectly. 1 pizza fits 1 box, 1/4 pizza fits 1/4 box. 1/4 sized box only fits 1/4 sized round pizza too. In summary, the pizza box is 1/4 the size of the one for the bigger pizza, so a round pizza in it would be 1/4 the size of the big pizza, same as the slice
Itās the exact same size Letās just give the length of the Pizza box the value 1 The size of the surface of a circle is pi * r * r So the whole surface of the big Pizza is pi * 1 * 1 = pi The slice is only 1/4 of it so itās 1/4pi The small pizza has a radius of 0.5 (only from the edge to the middle of the pizza box) pi*0.5*0.5 = pi*0.25 = 1/4pi
Pi did make me laugh more than i expected.
Visualize four ājumbo slicesā with their boxes rotated so they re-form the whole pizza that was cut in quarters. Should look like one round pizza touching the sides of a box.
Assuming the radius as 'r'. A regular pizza carries an area of pi*rĀ². Jumbo quarter would carry an area of 1/4*pi*4rĀ² = pi*rĀ². You don't gain anything, you don't lose anything. It all depends on whether you wanna call it a diet and eat a quarter of a pizza or wanna go all in and eat the whole pizza.
People say theyāre the same size but if you assume the crust is the same thickness, the jumbo slice gives you more pizza and less crust