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Discussion Starter · #1 ·
OK, here's a little trick I just realized.


Do you want to know the area of your 16:9 screen, in square feet? Just take the diagonal measurement, in inches, square it, and divide by 337.


Examples:


100" diagonal: area = 100 * 100 / 337 = 29.67 sq. ft.

120" diagonal: area = 120 * 120 / 337 = 42.73 sq. ft.


Believe it or not, this is exact, though only for 16:9 screens. The numbers just work out that way. This may not seem like a big deal to you but frankly I was tired of having to jump through some Pythagorean hoops to calculate the width and height of a screen from its diagonal, convert them to feet, then multiply them together.


If you want to compute your screen brightness in foot-lamberts, just take the calibrated brightness of your projector, in ANSI lumens, multiply by the screen gain, multiply by 337, then divide by the diagonal size (in inches), twice.


Example:


120" diagonal StudioTek 130, 600 calibrated lumens:

brightness = 600 * 1.3 * 337 / 120 / 120 = 18.25 ft-L.


Again, this is exact, but only for 16:9 projectors on 16:9 screens.


See? 337 is a home theater nut's favorite number.


Just remember it. 337. 337. 337. It will never lead you wrong.


Until you get a 2.35:1 screen.
 

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My experience with 337: I drew a 9x16 rectangle, with a 9x12 rectangle imbedded to one side. Why? If you know a 16x9 TV screen diagonal size D, the 4x3 image diagonal will be 15D/sqr(337) for viewing nonHD material.


Scaling the rectangle by the factor d, where d is arbitrary, a 9dx16d rectangle has an area of 144dd = 12d*12d and a hypotenuse of d*sqr(337). So if your measurement of the diagonal is d*sqr(337) = D, the area is A=144dd. But from the first equation d=D/sqr(337). So A=144*DD/337 and if you measure in inches and want sq. ft., then A'=A/144=DD/337. But, hey, you already knew that.


So, yes, the scheme works since 144=9*16=12*12.
 

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I'm sure there's a quicker way ... but here goes


c = diag in inch

A = width in feet

a = width in inches

B = height in feet

b = height in inches


trying to prove (c^2)/337 = A * B


start at


c^2 = (a^2)+(b^2)


b in terms of a


b/a = 9/16

b = (9*a)/16


substitute


c^2 = (a^2) + (9a/16)^2


multiply out


c^2 = 337(a^2)/256


move factor of 337


(c^2)/337 = (a^2)/256


replace inches with feet and substitute one of the a's


a = A*12

and

a = 16b/9

a = 16*(B*12)/9


(c^2)/337 = (A*12)*(16*(B*12)/9)/256


multiply out


(c^2)/337 = A * B ;)
 

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Discussion Starter · #6 ·
I knew I was in the company of fellow math geeks. Glad to know ya :) But for those out there for whom algebra is just a bunch of gibberish, just trust the 337 trick. These guys vouch for it. :)
 

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Discussion Starter · #8 ·
From the other thread I posted on this, there are "magic numbers" for other screen shapes too:


4:3 -> 300

16:9 -> 337

2.35:1 -> 399.6766 ~ 400


In general:


x:y -> (x/y+y/x)*144


Of course, if you start computing magic numbers for every shape screen the "magic" sort of fades. This works precisely because it's easy to remember a single number.
 
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