It's Greek
The terms Pythagorean Theorem and Pythagoras’ Theorem refer to the same principle. Pythagoras was a Greek mathematician and philosopher born in Samos in 575 B.C.E. He created the formula a2 + b2 = c2 used in geometry classes around the world every day.
Right Triangles
Look at a right triangle (a triangle where one of the angles is 90 degrees) and notice one side of the triangle will be noticeably longer than the other two sides. The long side is referred to as the “hypotenuse.” If the Greek vocabulary gets confusing try to remember that “tenuse” part means “stretched.” So the hypotenuse is the line stretched over the right angle. The other two lines are called the legs of the triangle. In the formula “a” and “b” are the legs and “c” is the hypotenuse.
The Proof
Pythagoras recorded a proof of an idea that ancient peoples, such as Babylonians, Egyptians and Indians, had already discovered and used in their understanding of the world around them. The idea that the lines in a right triangle had a special relationship to each other certainly was nothing new by the time Pythagoras created the mathematical formula.
Pythagorean Triples
These are sets of number such as 3, 4, 5 and 5, 12, 13 and 11, 60, 61 which will work as the numbers for “a”, “b” and “c.” in the formula a2 + b2 = c2 . Knowing some of the common triples is a great shortcut to figuring out problems using the Pythagoras Theorem. It is also helpful to know that any multiple of a triple will also be a triple. Here is an example of using a multiplier of a triple in the Pythagorean Theorem, k32 +k42 =k52. So if k equals 2 and you use the triplet (3, 4, 5) you would know that 62 + 82 = 102 and using the triplet (5, 12, 13) means 102 + 242 = 262
Applying the Theorem to Everyday Life
The Pythagorean theorem is useful if you want to make a ramp of the proper length or when deciding how to aim if you're playing pool.
Getting more Help
If you want more help with the Pythagorean Theorem or any other geometric proofs, please give us a call at Mathnasium of Parker 303-840-1184. Try one of our free trial sessions and experience how stress free geometry or other math homework can be.
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