Software Steeplechase

With prices continuing to drop, I’ve been looking into upgrading my television to a wide screen flat panel model. Besides high-definition, I’ve also been looking forward to an increase in raw size that a new TV will offer, but what constitutes an increase in size? A 32 inch television with an aspect ratio of 4 by 3 has a larger viewing area than a 32 inch 16 by 9 (wide screen) TV, since the dimension is that of the hypotenuse of the corners.

For example, if you were to ’stuff’ a 16x9 image into a 4x3 TV set, it doesn’t fit. You have to scale the image down in order to preserve the aspect ratio. This scaling down is what creates the letter boxing above and below the image. In the example below, you can see how a 36 inch television is capable of displaying a wide screen image that is the same physical dimensions that would result from a 32 inch wide screen TV displaying that image.

Screen-sizes alone are poor indicators of the raw picture size unless we are comparing television sets that have the same dimensions. So, in order to compare these apples and oranges, you need the idea of a scalar. A scalar can be used to bridge the gap between comparing the wide screen TVs with the televisions many of us are used to. In the previous example, our scalar would be 1.25 or %12.5 since you need a 4by3 TV that is %12.5 bigger than a wide screen TV in order to display the exact same picture size.

When displaying a 4x3 image in a wide screen TV, the same scaling takes place, but now it is the 4by3 image that is being scaled down to fit inside of the 16x9 aspect ratio of the wide screen TV. This results in the vertical letter boxing depicted below.

So if I upgrade to a wide screen TV, I surely don’t want to view a picture broadcast in a 4x3 ratio in a size that is physically smaller than the image I would have seen in my “old-fashioned” television. Therefore, what size wide screen TV do you need to ensure that the 4x3 images are at least as big as they were on your old set?

1) When normalized with the 16x9 ratio, the 4x3 ratio becomes 12x9.
2) Using the good old Pythagorean theorem, we can find a hypotenuse of ratio 15 for the 12x9 (4x3) set, and a ratio of 18.358 for the 16x9 set.
3) Dividing 18.358 by 15 results in a scalar of about %122 or 1.22
4) To find the minimum size wide screen TV you would need in order to match the raw picture size of your 4x3 TV, just multiply the size of your 4x3 TV by 1.22.

For example, if you currently have a 27 inch television, you would need a wide screen TV that is at least 27 X 1.22 = 33 inches in order to prevent having a smaller image on your new TV set.

I hope you find this scalar useful when shopping for your new television/monitor so that you don’t end up with a smaller image than what you had!