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# Video:What Is Pythagoras' Theorem?

with Jen D'Amore

The Pythagorean theorem is a historical formula used to evaluate the measurements in right triangles. Though the theorem is centuries old, it still applies to modern math. Learn more about the Pythagorean theorem in this video.See Transcript

## Transcript:What Is Pythagoras' Theorem?

Hi, I'm Jen D'Amore for About.com, and this video is all about the Pythagorean theorem.

Around 500 BC Pythagoras, a Greek philosopher with a fascination for numbers and a determination to show the geometric basis of everything in nature, started his own school, sometimes referred to as a brotherhood, or cult of math, the participants of which then called the Pythagorans. It has been suggested that Pythagoras was inspired by visiting the great pyramids in Giza.

Studying their symmetry and the relationships between lines and shapes may have led him to what is now known as the Pythagorean theorem. Though there is debate as to whether he, one of his math brothers, or someone further back in history was the first to discover it, the theorem still bears his name.

### Pythagoras' Theorem Applies to Right Triangles

The theorem states that with any right triangle, the area of the square of the hypotenuse equals the sum of the areas of the squares of the remaining sides or:a squared + b squared = c squared. A simple numerical demonstration of this can be done with a right triangle that has a hypotenuse with a measurement of 5, one leg that measures 4, and one leg that measures 3. Plug that into the equation and solve.But rather than staring at numbers, try drawing it out. Start with a right triangle, label each side, making sure that the hypotenuse, that the side across from the right angle, is "C" then show the square of each side. This is a squared, this is b squared and this is c squared. So according to the theorem, these two squares, a squared and b squared will add up to this larger square, c squared.

Various "proofs" of the the theorem exist, some are visual geometric studies, others are algebraic interpretations. Probably the earliest known proof is usually referred to as "the Chinese proof" and dates back to 1000 BC. The relationships between these shapes can also be seen in early Babylonian tiles. Bhaskara's proof is a dissection proof that came from India in the second century A.D. Starting with this diagram, what we are looking at is c squared, since the hypotenuse completely makes up the length of the square. By re-arranging the shapes, you can turn c squared, into a squared + b squared.

### Learn How to Use the Pythagoras' Theorem

Now that it's starting to make sense, we can return to the formula for daily use. Let's say you're locked out, you need to climb into a second story window, and you want to figure out how long a ladder you need. The window is 10 feet above the ground, the ladder will need to be angled to climb, and the most solid ground is 5 feet from the wall. plugging that into the equation 10 squared + 5 squared = c squared which after solving gives us c = 11.18ft, so you'll need a ladder that is at least 11.18 ft.

Luckily, your neighbor has a 12ft ladder that will work just right. Here's another example. You're re-routing a race that goes through town, but one area where competitors used to run around a block of buildings has been torn down and they can now run on the diagonal through it. To figure out the new distance so you're training can be consistent, plug in what you know. The Length of each block is 1000 meters and 300 meters. So, the new diagonal distance is 1044 meters.The pythagorean theorem is typically taught between grades 6 - 10, depending on the student's math proficiency.Thanks for watching. To learn more visit us on the web at About.com.
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