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 04-26-2021, 05:12 AM #61 Balor Patch   Join Date: Apr 2013 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
04-26-2021, 05:17 AM   #62
maximara
On Notice

Join Date: Aug 2004
Location: Sumter, SC
Re: GURPS Realm Management

Quote:
 Originally Posted by Balor Patch 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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 04-26-2021, 01:01 PM #63 Anthony   Join Date: Feb 2005 Location: Berkeley, CA 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. __________________ My GURPS site and Blog. Last edited by Anthony; 04-26-2021 at 01:04 PM.
04-27-2021, 03:11 AM   #64
maximara
On Notice

Join Date: Aug 2004
Location: Sumter, SC
Re: GURPS Realm Management

Quote:
 Originally Posted by Anthony 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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 04-27-2021, 04:12 AM #65 maximara On Notice     Join Date: Aug 2004 Location: Sumter, SC 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). __________________ Help make a digital reference for GURPS by coming to the GURPS wiki and provide some information and links. Please, provide more then just a title and a page number.

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