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Contents
Pythagoras Theorem
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Pythagoras Theorem
Pythagoras Theorem The Pythagoras Theorem is one of the most important mathematical contributions. Although it is named after Pythagoras, a Greek mathematician and philosopher, ancient civilisations already knew it, like the Babylonians. However, Pythagoras may have been the first to prove it. The Pythagoras Theorem states that The area of the square built upon the hypotenuse of a right triangle is equal to the sum of the squares built upon the remaining sides. In simple terms, given the right-angled triangle
a2 + b2 = c2
Applications of the Pythagoras Theorem The Pythagoras Theorem has many uses, both mathematical and practical. Mathematical uses include geometry--the calculation areas and volumes. It is also used on the cartesian plane in analytic geometry and calculus. More importantly, it is an integral concept in the definition of the trigonometric functions--the sine, cosine and tangent functions are the ratios of the lengths of sides in a right-angled triangle. It is also the idea behind the fundamental identity of trigonometry--sin2x + cos2x = 1. Practical uses abound too. It is important in navigation, cartography, and also finding angles of elevation and depression. When we deal with right angles in every day life, it is highly likely that the Pythagoras Theorem will come in useful. In this section, we will show two proofs of the theorem, as well as a highlight on Pythagorean triples. Note that there are actually many proofs to the theorem--a whole website can be created solely on them! There are about 300 proofs involving real numbers, and if the entire complex number system is considered, there are about 500 proofs. You'll need the Shockwave plug-in to view the proofs. The plug-in can be downloaded from the Macromedia website without additional cost.
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