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April 4th, 2008, 06:04 PM   #1
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I'm Stumped

I want to solve the following equation for b:

(b*r)^2 + b^2 = c^2

This equation is similar to the Pythagorean theorem, except that "a" is replaced with "b*r", r being a ratio.

I have wasted 5 sheets of paper trying to solve for b, to no avail.

If you assume:

c = 10 and r = 4/3

Then "b" should yield 6.

I feel stupid. Thanks.
bretttolbert is offline  
 
April 4th, 2008, 06:58 PM   #2
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(b*r)^2=(b^2)*(r^2)
because exponents distribute over multiplication.
so:

(b*r)^2+b^2=c^2
b^2*r^2+b^2=c^2
(r^2+1)(b^2)=c^2

And you should be able to take it from there.

Cheers.
cknapp is offline  
April 5th, 2008, 07:33 AM   #3
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thanks, got it

Thanks for the tip. I finished up and solved for b.

b = sqrt( c^2 / ( r^2 + 1 ) )


I need to read up on my math rules.

I'm going to use this formula in a software program that calculates the viewable screen area and DPI resolution of LCD Monitors given the diagonal measure and native screen resolution.

I can get the ratio ("r") of any display by dividing the horizontal resolution ("x") by the vertical ("y") and using the diagonal measure ("c") I can determine the height ("b") and width ("b*r") of the monitor and multiply them together to get screen area.

And to get DPI, I just use:

dpi = sqrt( x^2 + y^2 ) / c

I just thought you might me interested in what the formula was for.

Thanks for your help.
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April 5th, 2008, 11:46 AM   #4
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Yeah those rules are things that become intuitive after a while... but it's really easy to forget that they're intuitive...
unless you work with set theory or higher algebra, where they aren't guaranteed...

Anyway, that's a clever way of handling screen resolution. I assume everything is going to be scaled to fit the screen properly?

I suddenly remember why I stick with theoretical CS...
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April 5th, 2008, 12:15 PM   #5
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Re: I'm Stumped

(br)² + b²
= c²
= b²r² + b²
= b²(r² + 1)


= c² / (r² + 1)

b(c,r)
= ±c / √(r² + 1), where the function is in two variables.


b(10, 4/3)
= ±10 / √(16/9 + 1)
= ±10 / (5 / 3)
= ±6
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