Which Screen Shape?

Source: Consumer Reports December 2003
in the Mathematics Teacher September 2004

Direct-view HD [high-definition] sets come in two aspect ratios: the familiar squarish 4:3 shape and the newer wide-screen 16:9 shape.   TV programming is usually formatted for a 4:3 screen, but more shows are adopting the 16:9 format.   Most cinematic movies are in a wide-screen format that's better suited for a 16:9 TV.   Content formatted for one screen type has to be modified to fit the other, so you may see bars on the sides or on the top and bottom of the images.   Most sets can stretch or crop images to eliminate bars.

Note that screen sizes aren't directly comparable.   Wide-screen 16:9 sets often measure 30 or 34 inches diagonally, while 4:3 screens generally measure 27, 32, or 36 inches diagonally.   Because of the differing proportions, a wide screen has roughly the same viewable areas as a square screen with a smaller diagonal measurement.   So a 34-inch wide-screen set might only have as much viewable area as a 32-inch 4:3 TV.

  1. The aspect ratios indicate the ratio of width to height.   Draw two rectangles, one with an aspect ratio of 4:3 and the other with a ratio of 16:9.

  2. Which ratio is greater, 4:3 or 16:9?   Why does the difference in these ratios matter in the context of television sets?

  3. In square inches, what is the viewable area of a 16:9 screen with a 34-inch diagonal measurement?

  4. In square inches, what is the viewable area of a 4:3 screen with a 32-inch diagonal measurement?

  5. As the article implies, does a screen television with a 34-inch-wide screen have as much viewable area as a 32-inch 4:3 television?

  6. If a show formatted with a 16:9 aspect ratio is viewed on a 4:3 screen, the picture will fill the screen horizontally, but bars will appear above and below the picture.   What portion of a 4:3 screen is filled by a 16:9 picture?

  7. If a show formatted with a 4:3 aspect ratio is viewed on a 16:9 screen, the picture will fill the screen vertically, but bars will appear on either side of the picture.   What portion of a 16:9 is filled by a 4:3 picture?