So I was bored and decided I wanted to know the width and height of my TV screen. I did some simple math and figured out a universal formula to figure out the width and height of a 16:9 square pixel monitor/TV.
The formula is:
(16/9(c/((√337)/9)))² + (c/((√337)/9))² = c²
Where c is the (most commonly advertised) diagonal lenth of your screen. Eg. “A 32-inch flat screen TV.”
I broke down the formula so it basically follows the Pythagorean theorem (a² + b² = c²). So the group in parentheses to the left of the + is the formula for a, the parentheses after the + is the formula for b and c is given.
So for instance solving the width (a) and height (b) of a 46" © flatscreen TV :
• (16/9(46/(18.35756/9)))² + (46/(18.35756/9))² = 2116
• (1.777778(46/(2.039729)))² + (46/(2.039729))² = 2116
• (1.777778(22.55202))² + (22.55202)² = 2116
• (40.09248)² + (22.55202)² ~ 2116
So now we have:
• a (the width) as 40.09248"
• b (the height) as 22.55202"
To test, finish the formula:
• (40.09248)² + (22.55202)² ~ 2116
• 1,607.407 + 508.5936 = 2116.001
So 2116.001 is about equal to 2116 (or 46²).