Just about everyone seems enthralled by all things digital – iPods, digital cameras, and so on. But hardly anyone stops to think about the math that’s behind the digital craze. About a year ago, I started introducing examples using references to digital items that students are familiar with. They perked up – “hey – this is something I can relate to…”

One of the really interesting examples I use is the “Myth of the Megapixels”. Ask anyone about digital cameras and they’re likely to tell you that more the megapixels, the better the camera. Well, this is not necessarily true. David Pogue, of The New York Times, posted an article about this. Here’s a small excerpt:

Let me tease you first with this question: How much bigger can I print a 10-megapixel photo than a 5-megapixel photo?

Most people answer, “twice as big” or even “four times as big.”

People assume that the length and width of the picture will be doubled.
He shows the math in his article. The gist of the calculation is this: the megapixels refer to the number of pixels in the area of the picture. So even if the area (number of pixels) was doubled, the length and the width of the picture are not doubled. For if the length and the width of the picture were doubled, the area of the picture would be four times as much, not twice. Here are Pogue’s calculations:

A 5-megapixel photo might measure 1944 x 2592 pixels. When printed at, say, 180 dots per inch, that’s about 11 by 14 inches.

A 10-megapixel photo (2736 x 3648 pixels), meanwhile, yields a 180-dpi print that’s about 15 by 20 inches—under three inches more on each margin!

The reaction from my students, you ask? “I’ll remember that next time I go shopping.”
I don’t get that reaction when I teach a topic like completing the square!