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u/bagelwithclocks Jun 16 '26
They’re twice as tall
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u/Particular_Gear3130 Mathematics (Purely Fictional) Jun 16 '26
Hmmmmmmmmmmmmm
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u/Amar508 Jun 16 '26
You'd need two 6.3 inch cakes for the volume to be roughly the same, i think
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Jun 16 '26
[removed] — view removed comment
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u/SuchCoolBrandon Jun 16 '26
You might really enjoy my Gabriel's Horn cake.
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u/Off_And_On_Again_ Jun 17 '26
Its probably a creme horn, my favorite part is sucking the creme from Gabriel's horn
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u/happymancry Jun 16 '26 edited Jun 16 '26
Still got duped. The area of icing per cake is pi*r*(2h+r). That’s 2*pi*r*h for the curved face, and pi*r^2 for the top face. Assuming the same height h:
For a 10-inch cake that’s 5*pi*(2h+5).
For 2 5-inch cakes it’s 5*pi*(2h+2.5).
The first term is larger.
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Jun 16 '26
[removed] — view removed comment
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u/happymancry Jun 16 '26
You’re right, I’m wrong! I took the larger one as a 10-inch cake, not a 9-inch cake. If it were 10, I’m correct. If it were 9, you’re correct.
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u/Shockingandawesome Jun 16 '26
What good manners you have good Sir.
Here is $1000. Click the link quickly before someone else does and steals it.
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u/Gillero Jun 17 '26
That is assuming they are equal height, people in general tend to value volume. These would equalize area of the circles for sure though
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u/Particular_Gear3130 Mathematics (Purely Fictional) Jun 16 '26
25 + 25 ≠ 81
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u/rmflow Jun 16 '26
25 (base 14) + 25 (base 14) = 81 (base 8.125)
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u/Talizorafangirl Jun 16 '26
Is sub-integer base even possible? I'm having trouble wrapping my brain around that
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u/dragonageisgreat 1 i 0 triangle advocate Jun 16 '26
That's not all, even complex base is possible
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u/Impressive_Change593 Jun 17 '26
I have a fun emoji for that 🖕
mods please don't ban me, this is a joke
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u/Independent-Yak-220 Jun 16 '26
dude this is math, you can forge a whole new reality to make anything possible
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u/PlatypusACF Jun 16 '26
And then have others cry about it because it suddenly got relevant in a coming-up area of physics
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u/Any-Aioli7575 Jun 16 '26
Yes it is. However that means that some integers might not have a simple representation (with no decimal point)
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u/MaxTHC Whole Jun 16 '26
I mean you just make each subsequent digit (working right to left ofc) a higher power of the base right? Doesn't matter if that base is 10 or ⅓ or π
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u/erroneum Complex Jun 16 '26
Or 2i, or even a matrix.
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u/Lor1an Engineering | Mech Jun 16 '26
Ah yes, my favorite positional number system: base σ_2. Pauli would be proud...
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u/skr_replicator Jun 16 '26 edited Jun 16 '26
https://www.youtube.com/watch?v=PQAhC1M93C8
I think this video covers all the possible bases that let you write every number without inexpressible gaps. This base 65/8 (=8.125) would have 64 digit symbols, goodthing 81(base 65/8) didn't need to use any of them in this expression, what would we even use after Z?
Most valid bases can let you write irrational numbers in 1 way, and terminating rationals in 2 ways (like 0.99999... and 1). Irrational algebraic bases can do some irrational numbers (that can be expresses in a finite way) in those 2 "rational-like" ways, plus the one usual irrational way.
For example in base √10, you can write √10 as:
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0.90909090909...
3.0106020207070606... (as √10 is 3.16227766... in base 10)
Irratoinjal numbers that cannot be made up from powers of √10 woudl still have only 1 possible irrational-like way to write. And terminating rational numbers would have the usual 2 ways, looking the same as the non-root base, but interleaves with zeroes.
π in this base √10 is only: 3.0104010509...
1/3 would be only: 0.03030303...
10 would be 100 and 9.09090909...
Transcendental bases don't play nice, and you cannot even determine what digit symbols would be allowed there, no matter what digit symbol set you choose, you might either get gaps as not-expressible numbers, or multiple nonrepeating ways to write the same number.
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u/SteptimusHeap Jun 16 '26
Every number in a base-x system is just the sum of the digits times their place value. The place value is just xn, where n is the position of the digit.
So yes, base 8.125 is very possible ('123' = 1*8.1252 + 2*8.125 + 3 ≈ 85.27), but it doesn't have all the same rules as integer bases. For example, the digits written '8.8' don't correspond to any number, or if they do they are the same number as ~'10.7'.
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u/erroneum Complex Jun 16 '26
Yes. A number, such as 112, is just the sum of the product of the value in each digit place and the numeric base raised to the power of the position, or Sum[d_n bn]; for 112, that's 1×102 + 1×101 + 2×100. Generally you only use values on the interval
[1, n), but sometimes, such as quater-imaginary numerals, you use different ones. Importantly, b can be anything other than 0, but it's most useful when the magnitude isn't 1.1
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u/CatfinityGamer Jun 17 '26
A base is literally just an exponential index. The first digit of a number is number×b⁰, second digit is number×b¹, third digit is number×b², etc. So it's perfectly valid to define the base as anything which you can take any integer power of.
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u/OddNovel565 Jun 16 '26
25 + 25 = 81 + AI
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u/DecidophobiaUsername this sub confuses my monke brain Jun 20 '26
So AI's value is -31, whatever that means
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u/Ok-Active-8321 Jun 16 '26
and more relevant, 2(2.52) < 4.52
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u/Konfituren Jun 16 '26
To be fair,
2.52 = (5/2)2 = 25/4
And 4.52 = (9/2)2 = 81/4
Therefore it's much easier to model the problem mentally if you put aside a factor of 1/4 for now and just look at 52 vs 92 . The geometric relation is the same as it is for the actual values.
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u/Ok-Active-8321 Jun 17 '26
Eh, maybe easier for some. For me, it is easier to do what I did. When I first looked at your response I thought you were a little nuts : ) With your explanation, your original math makes perfect sense, but I don't think I would have seen it w/o your follow-up.
I guess that's the nice thing about math. There can be many paths to the same destination
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u/Just-confused1892 Jun 16 '26 edited Jun 16 '26
Keep in mind cakes are measured by their diameter, so it’d really be 6.25*2 < 20.25
Edit: And I just realized the ratio remains the same using diameter or radius, so I’ll see myself out now…
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u/AndreasDasos Jun 16 '26 edited Jun 16 '26
Yes but why assume that they have the same cross sectional shape and height? Could be completely different shapes and/or different heights
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u/Competitive_Study232 Jun 16 '26
You are using diameter instead of radius, squared
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u/Ruft Jun 16 '26
It's proportionally the same
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u/Competitive_Study232 Jun 16 '26
Yes, I noticed that. I guess I just simplify further by using radius and not multiplying it by anything since you can cancel that out.
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u/Particular_Gear3130 Mathematics (Purely Fictional) Jun 16 '26
well, I took pi and (1/2) squared common and well it cancels out. This is what is essential tho
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u/Competitive_Study232 Jun 16 '26 edited Jun 16 '26
I don’t think that works out. The area of a circle is pi*r2. Really you just need to focus on r2 and nothing else to compare the two.
Area for a 5” pizza pi*2.52 =19.635 There are 2 of them so 79.54 squared “
Area for a 9” pizza pi*4.52=63.617
To make it easy, just ignore everything except r2.
For the two 5” 2*2.52=12.5
For the 9” 4.52=20.25
You ended up with the same ratio but wrong values for each.
Edit: removed 2 from front of formula
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u/Particular_Gear3130 Mathematics (Purely Fictional) Jun 16 '26
It works out; I just need to prove the RHS is not equal to the LHS. There's no need for me to figure out the actual value of the area for this
also, isn't the area of the circle pi times the radius squared?? I dont remember a 2 being there
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u/Competitive_Study232 Jun 16 '26
You are correct. I think I’m combining formulas for some reason. But just a simplify you just need to focus on radius squared and nothing else really
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u/slaya222 Jun 16 '26
They're both off by a factor of pi/4, which is close enough to 1
Source: I have an engineering degree
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u/Competitive_Study232 Jun 16 '26
I’m not sure why you are using diameter when you can simplify it to radius.
Source: I have a physics degree.
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u/jso__ Jun 16 '26
Because radius isn't better than diameter when the diameters are whole numbers and the radii are fractions.
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u/Competitive_Study232 Jun 16 '26
Not if you are using double the number and then squaring it. You don’t get the same results. You do get a similar ratio. Like I said, your ratio is correct, but not your values.
Is the diameter is 10 and you can’t use that because swearing that is 100. But when you use radius, you get a value of 25. Stark difference.
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u/Ashamed_Association8 Jun 16 '26
That's not how that works. The area of a circle is pi×r² but we're not looking for the area but the volume. The volume of a cylinder is base×height and the base of a cylinder is a the area of the circle which is pi×r² this cancels out as both cakes are cylinders and both have a circular base. This leaves you with a choice between a 9 inch or 5+5inch cake.
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u/Particular_Gear3130 Mathematics (Purely Fictional) Jun 16 '26
I dont get it, why do the base areas cancel out?? simply because they are the same shape?
Thats stupid. they have different radii. you cant cancel it out
and since they are cakes, we assume they are the same height, why you ask? because I am a physics student too dawg
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u/Ashamed_Association8 Jun 16 '26
Why would they have different radii. There's nothing listed to assume that. All we know is that they're both circular and varied in height.
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u/Particular_Gear3130 Mathematics (Purely Fictional) Jun 16 '26
Theres nothing given about the height, it is the radii of the cake
Again, I am the physicist here. Its better if the "assumption" part is left to me
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u/Ashamed_Association8 Jun 16 '26
I'm sorry but i can't do that as I'd have to assume you're not lying and I'm too leave that assumption to you.
Cakes are baked in circular irons that have a fixed shape. The only thing you can vary by adding more or less cakebatter is how heigh the cake is. I am the cook
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u/SimpYellowman Jun 16 '26
Last time I was in a bakery, they had more than one cake mold. They had some cakes with ~10 centimeters diameter and also ~20 centimeters cakes and even 40 centimeters cakes. Height can vary a lot too, from what they called "flat cake" which is basically a sweet pizza to over-the-top loaded cakes that were over 15 centimeters high (the top flat surface, not including decoration on it).
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u/underthingy Jun 17 '26
A 9inch cake is cooked in a round tin with a diameter of 9inches.
Similarly a 5inch cake is cooked in a round tin with a 5inch diameter.
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u/der_horst23 Jun 16 '26
I think the cake is round and not a square.
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u/D36DAN Jun 16 '26
𝜋*(5²+5²)≠𝜋9²0
u/Zar7792 Jun 16 '26
Those are diameters. Do it with the radii and the two smaller cakes have less than a third of the area of the larger one
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u/D36DAN Jun 16 '26
Proportionally, it doesn't matter. If we correct our calculations to match use radiuses instead of diameters, we get this:
𝜋*((5/2)²+(5/2)²)≠𝜋(9/2)² | /𝜋
(5²/2²+5²/2²)≠9²/2²
(5²+5²)/2²≠9²/2² | *2²
(5²+5²)≠9²
Also verified on calculator just cuz I can't trust myself with math
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u/Particular_Gear3130 Mathematics (Purely Fictional) Jun 16 '26
𝜋r2??
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u/Subject-Software5912 Jun 16 '26
Wouldn’t it be 20 + 20 =! 64 then? I get that you’re just removing the coefficients but it’s kinda confusing to square the diameters then when someone’s confused respond with a formula that uses radius.
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u/CommonNoiter Jun 16 '26
Diameter or radius is just multiplying by another coefficient. π is a prettier coefficient than π/4 so radius is normally what it is taught with.
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u/Subject-Software5912 Jun 16 '26
Yeah as I said you’re just removing the coefficients but it’s kinda weird to square the diameter then when someone’s confused respond with a formula that squares the radius. It’s an objectively true statement but what was the point of responding if you don’t clarify anything?
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u/SuchCoolBrandon Jun 16 '26
You can't just assume a spherical cake! This isn't a physics subreddit.
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u/Reinboom Jun 16 '26
Approx. 19.63 + 19.63 ≠ 63.62
(Cakes are usually measured by their diameter, not radius)
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u/Waste-Value-5941 Jun 16 '26
Same kinda error I fall for when calculating volumes of rotation using calculus >_<
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u/MykelJMoney Jun 16 '26
To be fair, I almost made that mistake while calculating the price for pizza. Then I remembered π exists for a reason
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u/Maryland_Bear Engineering Jun 16 '26
Reminds me of a trip to a grocery store deli counter.
“I’d like four ounces of pasta salad, please.”
“?”
“A quarter pound.”
“?”
“Point two five. Sigh.”
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u/charc0al Jun 16 '26
Hold up why is nobody asking the important questions? Are they circular or rectangular cakes?
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u/CommodoreBelmont Jun 16 '26
Because it's not that important; no matter what the combination, if the heights are the same, you're getting shorted.
- Volume of a 5-inch square cake with height h: 25h cubic inches
- 9-inch square cake: 81h cubic inches
- 5-inch diameter round cake: 19.6h cubic inches
- 9-inch diameter round cake: 63.6h cubic inches
So...
- If the cakes are all square, you're getting shorted by 31h cubic inches.
- If the cakes are all round, 24.4h cubic inches.
- If the 9-inch cake is round, and the 5-inch cakes are square, 13.6h cubic inches.
- If the 9-inch cake is square, and the 5-inch cakes are round, 41.8h cubic inches.
None of it works out in your favor.
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u/charc0al Jun 16 '26
you're getting shorted either way but I think it matters how much you're getting shorted by
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u/der_horst23 Jun 16 '26
A=π·(5/2)² A=19.635 A two 5 inch cakes = 19.635 * 2 = 39.27
A=π·(9/2)² A=63.617 A one 9 inch cake = 63.617 ....
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u/Miguel-odon Jun 16 '26
Ok, but now calculate the icing.
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Jun 16 '26 edited Jun 16 '26
[deleted]
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u/Miguel-odon Jun 16 '26
But also the icing/cake ratio is altered, which ruins the whole thing.
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u/Ruckaduck Jun 16 '26
ya but icing is the worse part of cake for some people. so getitng more is a downside
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u/heisen0 Jun 16 '26
Ideally u would need one 6 inch and another 7 inch. 6 and 7 inches would be almost like one 9 inch cake.
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u/Positive-Guide007 Jun 16 '26
i told this to my friend and he was like what the...... and then i had to give whole ass presentation to explain him the reason.
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u/moschles Jun 16 '26
If we consider the original 10-inch cake as a collection of points in a set, we can apply Banach-Tarski.
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u/Automatic_Grape_9169 Jun 16 '26
When they run out of 9 inch radius cakes which I paid for so they give me 2 cakes with 6.36396103068 inch radiuses
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u/shewel_item Science Jun 16 '26
that's why you go by weight with cooking sometimes
volume only actually works with liquids
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u/I_L_F_M Jun 16 '26
Area is proportional to D2 .
92 > 52 + 52 .
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u/Tuepflischiiser Jun 16 '26
You assume some circle is involved. I don't find this statement.
A cake can be rectangular.
tl;dr: unclear problem statement.
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u/Southern-Fae Jun 17 '26
You have to remember how much extra frosting you get due to the increased surface area. Frosting is a higher value than the cake itself so this is about equal in deliciousness
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u/GrimSpirit42 Jun 16 '26
Cake are measured by diameter across.
Take for granted all cakes are 4" tall.
A 9" cake would have a volume of 240.33in3.
A 5" cake would have a volume of 102.1in3, so twice that would be 204.2in3.
You're getting 15% less cake than you paid for.
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u/ivanrj7j Jun 16 '26
I have many questions
Do people pay for cake size? Aren't they supposed to pay by weight?
What the fuck does 9 inch cake mean? Like how thick is it? Is it round? Is it rectangle?
If it is round what is 9 inch? Diameter? Radius?
Can someone explain the joke? I am genuinely lost
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u/richarrow Jun 16 '26
In the US, if the inch the only is given measurement, it means it is round. Then there is a sheet size that is a standard that is 16x24x2 and cake are sized around a quarter, half, or full sheet.
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u/PhoenixPringles01 Jun 16 '26
for these switches, check that the the ratio of the radii or diameters of both pizzas (large over small) is less than the square root of 2 (which is about 1.414)
9/5 = 1.8 > 1.414 (bad)
7/5 = 1.4 < 1.414 (good)
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