Pythagoras

Pythagoras changed the world in the sense that nature could be explained and defined in a Mathamatical formula

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Today we particularly remember Pythagoras for the famous geometric theory he determined, showing that the rule of a right-angled triangle is governed by numbers. Although the theorem, now not known as Pythagoras' theorem, was known to the Babylonians 1000 years earlier, he may have been the first to prove it. The theorem of Pythagoras- often known as the a2 + b2 = c2 theorem, states that if you take the shortest side of a right triangle and multiply it by itself you get a2 (pronounced "A squared"). Then you can take the medium length side and multiply it by itself to get b2. If you add those two results together you get c2. For a right angled triangle the sqyuare on the hypotenuse is equal to the sum of the square of the opposite and adjacent angles. To theorise that the sum of two squares is equal to the third square meant that it was possible to cut up the two squares and reassemble them to from a square indentical to that of the third. For this theory to be proven, a right triangle(a triangle with 1 interior angle 90�). As shown in the diagram above, the mathematical equation for the Pythagorean Theorem is(where "c" is the hypotenuse): c2=a2+b2. The basis for the formula dated back from 2000 B.C Ancient Egyptians wanted to lay out square (90�) corners for their fields. they then discovered the"magic 3-4-5" triangle (right triangle). Egyptian workmen took a loop of rope knotted into 12 equal spaces(3+4+5=12); they took 3 stakes (three angles, thus making a triangle) and stretched the rope around them, they placed the stakes so the triangle had sides of 3-4&5 units. The side with 5 units is what we now know today as the hypotenuse( the longest side),and the angle opposite it was a right angle.The Ancient Greeks learnt this from the Egyptians. Between 500 and 350B.C. the Pythagoras analysed the 3-4-5 triangle and he and his followers began to think of the triangle's sides as the sides of 3 squares(the area of a square is a side multiplied by itself-squared2). In the 3-4-5 triangle, the area of a square of which it's hypotenuse is a side equals= the sum of the areas of the squares of the other 2 sides: 5X5=3X3+4X4 (25=9+16)(So if you say 5=c, 3=a, 4=b,then you come up with Pythagoras' Theorem: c2=a2+b2).The Pythagoreans then generalised this 3-4-5 triangle rule, and applied it to all right triangles. From there on in, that statement has been known as Pythagoras' Theorem... Copyright � 2001 Adrian and Kim Inc. All rights reserved. Hosted by www.Geocities.ws