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Pythagorean Theorem and Pythagorean Triples

Square of the hypotenuse equals the sum of the squares of the legs.

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Pythagoras TV

Credit: Robert Lopez
Source: CK-12 Foundation
License: CC BY-NC 3.0

Why isn’t your 48-inch television four feet wide? Why does a 7-inch tablet seem so small? When retailers give you the size of a screen, they’re giving you the length of the diagonal, not the width of the screen.

A Relic of History

It may seem odd that we measure screens in terms of diagonals. After all, we give the size of most rectangular objects in terms of length and width. The diagonal measurements are leftover from the first television screens. The earliest screens were actually circular, so manufacturers began measuring a screen by its diameter, or the distance across the circle.

Credit: Laura Guerin
Source: CK-12 Foundation
License: CC BY-NC 3.0

When television designs changed, retailers kept measuring across the diagonal. Today, it's not enough to know the diagonal measurement of a screen. In order to figure out its width and height, you also need to know the aspect ratio (the ratio of the width to the height). For televisions with a 4:3 aspect ratio, the side and diagonal measurements are proportional to those of a 3-4-5 right triangle. This means that a 15-inch television with a 4:3 aspect ratio will be 12 inches wide and 9 inches tall. High-definition (HD) televisions are built on a 16:9 aspect ratio, so a 48-inch HD TV would be about 42 inches wide and 24 inches tall.

How big of a television do you need? It depends on where you want to put it and how you want to use it.

See for yourself: https://www.youtube.com/watch?v=JID7aKPzpIA 

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We've come a long way from the circular screens of the early 1950s, and television technology is continually improving. What’s next for our screens? Check out the links below to find out.




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Image Attributions

  1. [1]^ Credit: Robert Lopez; Source: CK-12 Foundation; License: CC BY-NC 3.0
  2. [2]^ Credit: Laura Guerin; Source: CK-12 Foundation; License: CC BY-NC 3.0

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