Scaling among nonequal values.

[xwhaletailx]

1) Start with two constants (k = 200 & h = 200). Then introduce two new variables, (a = 10.5 & b = 8.9). What I'm doing is scaling k and h equally, inversely and relative to the variables. So in this example, my equation would be c = (10.5-8.9)/(10.5+8.9). Then k = k*(1+c) and h = h*(1-c). Ultimately this gives me h = 183.5 and k = 216.5, which if divided, equates to 0.848 which is is equivalent to 8.9/10.5, right. This checks out.

2. Now what about when k and h are not equal? For example where k = 600 & h = 400 and still, a = 10.5 & b = 8.9. How do I cope with this and get the same result where k and h equally and inversely scale the right amount to equate to 8.9/10.5? Obviously k, being 600, would scale down in this scenario and h would scale up. How can I go about this? Thank you for any help.

 

[Otis]

… two constants (k = 200 & h = 200) …

h = 183.5 and k = 216.5 …

Hi xwhaletailx. Did you mean to say that k and h are variables? Constants do not change value. Maybe you need to use additional symbols.

You said symbols a and b are variables. So, their values vary.

Can you explain more about the scaling? What you're doing is not clear, to me. Does this have to do with proportionality, like map scales? What does symbol c represent?

?

 

[xwhaletailx]

Hi xwhaletailx. Did you mean to say that k and h are variables? Constants do not change value. Maybe you need to use additional symbols.

You said symbols a and b are variables. So, their values vary.

Can you explain more about the scaling? What you're doing is not clear, to me. Does this have to do with proportionality, like map scales? What does symbol c represent?

?

yeah I guess I meant variables for K and H and I just made C to show what is returned from that equation. Also A and B's values do vary. So think of it as two squares, both begin the same size (200 by 200 units). Then you input A and B, run that C equation which gives you two values scaling one square up and scaling one square down to proportionally represent 8.9/10.5 ratio. The equation works if the squares begin equal but I'm trying to figure out the equation if the squares do not begin equal.

 

[Otis]

… scaling one square up and scaling one square down to proportionally represent 8.9/10.5 ratio …

Hey there. So, there exist countless pairs of scaled h and k values where H/K=b/a (I'm using upper-case letters to represent the new values of h and k.) You seem to want the specific pair where h and k change by the same amount (which I'll call x).

H = h - x
K = k + x

If that's correct, then here's a formula for x (and it doesn't matter whether h=k or not).

x = (a·h ─ b·k) / (a + b)

Given h = 400, k = 600 (with a = 10.5 and b = 8.9) and rounding all results:

x = -58.7629

H = 400 - (-58.7629) = 458.76

K = 600 + (-58.7629) = 541.23

H/K = 0.8476

?

 

[xwhaletailx]

X actually equaled 58.7 but you knew that, just wrote it wrong. This works perfect. Thank you

 

[Otis]

X actually [equals] 58.7 but you knew that …

Yup (except for the sign) -- I copied the value from my confirmation of h=k, by mistake.

I'm not sure why signs are swapped, but I'm glad things work at your end (I'd posted -16.4948, but it's actually positive, for h=k. My value for h<k is -58.7629, yet you posted 58.7). Anyway, I'll edit that post. Thanks for the heads-up.