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Old 04-26-2021, 05:12 AM   #61
Balor Patch
 
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Default Re: GURPS Realm Management

Area = X/2 sq miles (to sync what we've been doing with the table on RM pg.4.)

Steps to getting size alone:
Area = (e^(ln(10)/6))^2)^size / 2
2*Area = (e^(ln(10)/6))^2)^size
ln(2*Area) = size * ln((e^(ln(10)/6))^2))
ln(2*Area) / ln((e^(ln(10)/6))^2)) = size

or:
ln(2*Area) / 0.767528364 = size
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Old 04-26-2021, 05:17 AM   #62
maximara
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Default Re: GURPS Realm Management

Quote:
Originally Posted by Balor Patch View Post
Area = X/2 sq miles (to sync what we've been doing with the table on RM pg.4.)

Steps to getting size alone:
Area = (e^(ln(10)/6))^2)^size / 2
2*Area = (e^(ln(10)/6))^2)^size
ln(2*Area) = size * ln((e^(ln(10)/6))^2))
ln(2*Area) / ln((e^(ln(10)/6))^2)) = size

or:
ln(2*Area) / 0.767528364 = size
Thanks, that is what I was looking for.
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Old 04-26-2021, 01:01 PM   #63
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Default Re: GURPS Realm Management

Why on earth express it as X = (EXP(LN(10)/6)^2)^Size instead of Power(10,Size/3)? The whole (EXP(LN(10)/6)^2) evaluates to the cube root of 10. Under the hood, power(x,y) is actually translated into exp(ln(x)*y) because for non-integer values of y it's much easier, but there's no need to expose it.
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Last edited by Anthony; 04-26-2021 at 01:04 PM.
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Old 04-27-2021, 03:11 AM   #64
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Default Re: GURPS Realm Management

Quote:
Originally Posted by Anthony View Post
Why on earth express it as X = (EXP(LN(10)/6)^2)^Size instead of Power(10,Size/3)? The whole (EXP(LN(10)/6)^2) evaluates to the cube root of 10. Under the hood, power(x,y) is actually translated into exp(ln(x)*y) because for non-integer values of y it's much easier, but there's no need to expose it.
So Area = X/2 actually becomes Area = e^(ln(10)*Size/3)/2?

2*Area = e^(ln(10)*Size/3)
ln(2*Area) = ln(10)*Size/3
(ln(2*Area) / ln(10)) * 3 = Size

That is a far saner equation. Thanks
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Old 04-27-2021, 04:12 AM   #65
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Default Re: GURPS Realm Management

Oh. While I am thinking of it what value was used for Krypton in the chart? In fact, Krypton has had so much variation that it was even used is puzzling.

For example, Krypton in Action #500 pg 31 is shown far larger than Earth (it appears to be double the diameter of Earth). In the early post Crisis DCU it was the size of Earth and in Superman Red Son it was Earth of the far future (And yes the "L" in Jor-L stands for exactly what you think it does).
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