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4:3 math vs 16:9 math

Posted by DavidLD (A) on August 18, 2007 at 05:22:37

Does anyone here know exactly when 4:3 became the standard aspect ratio for TV sets? Must have been earlier than 1950, at least 60 years ago. The math there is interesting, because 4:3 corresponds to the 3:4:5 ratio of a right triangle pythagoras theorem. That is, 3 squared is 9, 4 squared is 16 and the sum of those is 25 which just happens to be the square of (tada), 5!
That means, among other things, that if 4:3 had survived into big screen flat panels, a 50-inch diagonal flat panel would be exactly 30 inches high and 40 inches wide.

But now we have 16:9. That is no obvious ratio, it is often rounded to 1.78, but that isn't even accurate except to two decimal places. The problem is, film-makers dont film in 1.78. They film typically in 1.85 for "standard" movies, but wide-screen movies are typically 2.35 aspect ratio.

16:9 math gets more complex. For our 50-inch diagonal screen, its helpful to divide 2500 by 337, and then take the square root of that. The 2500 is 50 squared. Interestingly, 337 is the sum of 16 squared (256) and 9 squared (81).

The resultant number from this math multiplied by 16 gets you the width of the screen, or when multiplied by 9 gets you the height of the screen. YOu can of course use the same approach for other diagonal measurements, just square the diagonal measurement you want to use, and divide by 337. Then take the square root of that number to get your factor that gets multiplied by 16 or 9 to find the width or height.

A widescreen movie to DVD transfer typically will be at minimum 1.85, and often 2.35. Even the widescreen 1.85 results in small black bars at the top and bottom. In my large DVD collection, I've run into exactly 1 widescreen DVD that claims to have been redune to fit exactly 1.78, the movie "White Palace". The rest of the widescreens are either 1.85 or commonly 2.35 which results in fairly wide black bars on my 16:9 projection screen. I can fill the screen with the DVD player or projector zoom, but I lose the stuff on the edges then.

Meanwhile I go to the theater and am constantly watching them jockey around with power screen top and bottom or side curtain pulldowns and pull aparts to adjust the apparent height or width of the screen to fit what they are showing, the previews are typically 1.85, but the feature most often is 2.35. Many in the audience dont even seem to notice the foolishness.

Then occasionally the projectionist goofs and flips on the wronng anamorphic lens, which typically results in very tall and skinny actors.

In the 60s and 70s there were experiments in making widescreen movies on 70mm not 35mm film, but silver oxide film technology improved and it was cheaper to film everything on conventional 35mm film, using camera lenses to scrunch everything together horizontally, and then to have a anamorphic reconversion lens on the projector at the theater to unschrunch everything back to widescreen. Certaionly cheaper than having a different projector that could run 70mm wide film for the occasional movie filmed on 70mm for sure.

As I sit in the theater and watch all these gymnastics, from cheens changing aspect ratios at the flip of a button to projectionists who mistakenly run the 1.85 lens on a 2.35 movie, and think to myself that most of the time all these goings on work more or less flawlessly.

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