Random math question regard Square Cube Law
By
Ardrea,
Posted on: 2011-08-23 17:35 in Player Questions
n^3, where n is the increase in size (2 for double, 3 for triple, etc).
Consider a cube:
Volume (which corresponds to mass via density) = L x W x H
Double-sized volume = 2L x 2W x 2H = 8 x L x W x H
Triple-sized volume = 3L x 3W x 3H = 27 x L x W x H
And so on...
So your Excel formula would be weight x (percentage/100)^3.
"You don't lose levels. You don't have equipment to wear out, repair, or lose, or that anyone can steal from you. About the only thing lighter than debt they could do is have an NPC walk by, point and laugh before you can go to the hospital or base." -Memphis_Bill
We will honor the past, and fight to the last, it will be a good way to die...
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Thanks!
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Originally Posted by DarkGob
n^3, where n is the increase in size (2 for double, 3 for triple, etc).
Consider a cube: Volume (which corresponds to mass via density) = L x W x H Double-sized volume = 2L x 2W x 2H = 8 x L x W x H Triple-sized volume = 3L x 3W x 3H = 27 x L x W x H And so on... So your Excel formula would be weight x (percentage/100)^3. |
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Originally Posted by reiella
Until I see something that states to the contrary, going to assume VK is right
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I should add, and this mostly goes without saying but what the heck why not be precise, that the "percentage/100" part depends on how you're expressing your percentage. If you're already expressing it as a decimal, it would just be percentage^3.
"You don't lose levels. You don't have equipment to wear out, repair, or lose, or that anyone can steal from you. About the only thing lighter than debt they could do is have an NPC walk by, point and laugh before you can go to the hospital or base." -Memphis_Bill
We will honor the past, and fight to the last, it will be a good way to die...
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I have it in Excel as = Weight * ((New Height/Old Height)^3)
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Originally Posted by DarkGob
I should add, and this mostly goes without saying but what the heck why not be precise, that the "percentage/100" part depends on how you're expressing your percentage. If you're already expressing it as a decimal, it would just be percentage^3.
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Originally Posted by reiella
Until I see something that states to the contrary, going to assume VK is right
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That's reasonable.
"You don't lose levels. You don't have equipment to wear out, repair, or lose, or that anyone can steal from you. About the only thing lighter than debt they could do is have an NPC walk by, point and laugh before you can go to the hospital or base." -Memphis_Bill
We will honor the past, and fight to the last, it will be a good way to die...
*awaits a post from the Doyenne of Digits herself, Arcanaville*
If the game spit out 20 dollar bills people would complain that they weren't sequentially numbered. If they were sequentially numbered people would complain that they weren't random enough.
Black Pebble is my new hero.
Yes, I am also eagerly awaiting someone to swoop in and tell me how irredeemably wrong I am.
On another note, I didn't even know doyenne was a thing. TIL.
"You don't lose levels. You don't have equipment to wear out, repair, or lose, or that anyone can steal from you. About the only thing lighter than debt they could do is have an NPC walk by, point and laugh before you can go to the hospital or base." -Memphis_Bill
We will honor the past, and fight to the last, it will be a good way to die...
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She prefers grande dame des mathématiques
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Originally Posted by DarkGob
Yes, I am also eagerly awaiting someone to swoop in and tell me how irredeemably wrong I am.
On another note, I didn't even know doyenne was a thing. TIL. |
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Meh. I wasn't expecting her to swoop in and tell you how wrong you were, or even that you were wrong. She has enough people that she has to keep telling they are wrong as it is. She doesn't tell people that aren't wrong that they are wrong, so you should be safe here.|
Originally Posted by DarkGob
Yes, I am also eagerly awaiting someone to swoop in and tell me how irredeemably wrong I am.
On another note, I didn't even know doyenne was a thing. TIL. |
I was just waiting for her to come in and expand on what information had been given and do it in such a manner as to make my head spin.
If the game spit out 20 dollar bills people would complain that they weren't sequentially numbered. If they were sequentially numbered people would complain that they weren't random enough.
Black Pebble is my new hero.
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She spins you right round? |
Originally Posted by Texas Justice
Meh. I wasn't expecting her to swoop in and tell you how wrong you were, or even that you were wrong. She has enough people that she has to keep telling they are wrong as it is. She doesn't tell people that aren't wrong that they are wrong, so you should be safe here.
I was just waiting for her to come in and expand on what information had been given and do it in such a manner as to make my head spin. |
There I was between a rock and a hard place. Then I thought, "What am I doing on this side of the rock?"
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She certainly does.|
Originally Posted by Twisted Toon
She spins you right round?
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Of course, she's not worried about me stalking her for a few reasons.
There is a rather large wet area I'd have to traverse.
If I started getting anywhere in her vicinity she'd only have to say 1 or two sentences that begin to explain a complex mathematical theory and I'd be confused and stunned for hours. And unlike my Blasters, I have no ability to use my most basic abilities while in those states.
If the game spit out 20 dollar bills people would complain that they weren't sequentially numbered. If they were sequentially numbered people would complain that they weren't random enough.
Black Pebble is my new hero.
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There are just so many poorly chosen words in that sentence.
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Originally Posted by Texas Justice
She certainly does.
Of course, she's not worried about me stalking her for a few reasons. There is a rather large wet area I'd have to traverse. |
"You don't lose levels. You don't have equipment to wear out, repair, or lose, or that anyone can steal from you. About the only thing lighter than debt they could do is have an NPC walk by, point and laugh before you can go to the hospital or base." -Memphis_Bill
We will honor the past, and fight to the last, it will be a good way to die...
The key is to understand *why* doubling makes weight increase by 8.
That's because:
8 = 2^3 (aka 2*2*2)
Basically, here's how to think about it. Say you DON'T scale something proportionally. You just stretch it so it's twice as tall, but increase the amount of stuff so the density stays the same. Mass doubles, right? Twice as much stuff = twice as much stuff. Or say instead of "twice as tall" you did "twice as wide". Or "twice as deep". Same thing.
So think of scaling up height by a factor of two and keeping proportions as really being the same as doubling height, width, and depth. And that means *2, *2, *2. *8. And similarly, if you triple them all, you get *3, *3, *3, or *27.
HTH.
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They were rather carefully chosen.
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Originally Posted by DarkGob
There are just so many poorly chosen words in that sentence.
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If the game spit out 20 dollar bills people would complain that they weren't sequentially numbered. If they were sequentially numbered people would complain that they weren't random enough.
Black Pebble is my new hero.
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Yup, figured that out.
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Originally Posted by seebs
The key is to understand *why* doubling makes weight increase by 8.
That's because: 8 = 2^3 (aka 2*2*2) Basically, here's how to think about it. Say you DON'T scale something proportionally. You just stretch it so it's twice as tall, but increase the amount of stuff so the density stays the same. Mass doubles, right? Twice as much stuff = twice as much stuff. Or say instead of "twice as tall" you did "twice as wide". Or "twice as deep". Same thing. So think of scaling up height by a factor of two and keeping proportions as really being the same as doubling height, width, and depth. And that means *2, *2, *2. *8. And similarly, if you triple them all, you get *3, *3, *3, or *27. HTH. |
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Originally Posted by reiella
Until I see something that states to the contrary, going to assume VK is right
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All I know is that to me, she looks like she's lots of fun.
...oh, wait, we're talking about an actual person here? .
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So you think you're a hero, huh.
@Boltcutter in game.
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obligatory "no girls on the internet" remark
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Originally Posted by Fulmens
All I know is that to me, she looks like she's lots of fun.
...oh, wait, we're talking about an actual person here? . |
"You don't lose levels. You don't have equipment to wear out, repair, or lose, or that anyone can steal from you. About the only thing lighter than debt they could do is have an NPC walk by, point and laugh before you can go to the hospital or base." -Memphis_Bill
We will honor the past, and fight to the last, it will be a good way to die...
If this is in reference to real-world (or semi-real world?) creatures, it's more complex. Larger creatures need to maintain strength of bones and muscles, and if you simply multiply all the dimensions by the same factor, those strengthen something like the square of the factor, instead of by its cube. So, a humanoid exactly twice the size in height, width, and depth would be eight times heavier, but only four times stronger. So, to compensate, realistic creatures tend to get heavier-set as they're larger and larger. And still end up proportionately less nimble.
For some easy to understand discussion of this, try looking over wiki's article on Allometry.
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Yup, aware of that. As I said, fantasy setting. So magic can compensate where biology starts to fail.
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Originally Posted by Ardrea
If this is in reference to real-world (or semi-real world?) creatures, it's more complex. Larger creatures need to maintain strength of bones and muscles, and if you simply multiply all the dimensions by the same factor, those strengthen something like the square of the factor, instead of by its cube. So, a humanoid exactly twice the size in height, width, and depth would be eight times heavier, but only four times stronger. So, to compensate, realistic creatures tend to get heavier-set as they're larger and larger. And still end up proportionately less nimble.
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Originally Posted by reiella
Until I see something that states to the contrary, going to assume VK is right
. |
I know that doubling all measurements (essentially scaling up a living creature to twice it's original size and keeping everything exactly the same in ratio) results in an eightfold increase in mass.
My problem is I can't seem to figure out what the ratio would be for non-double increases in dimensions. All the formulae I can find are based on overall surface area.
Is it possible to make a formula that I can put into Excel or something with a weight and then a percentage increase of enlargement to find out what a scaled up version of the lifeform would weight at the new size?
I'm trying to calculate what the approximate size of a giant would be for a fantasy story I'm writing.