Trigonometry :: essays research papers

TrigonometryTrigonometry uses the fact that ratios of pairs of sides of triangles arefunctions of the angles. The basis for mensuration of triangles is the right- move triangle. The term trigonometry means literally the measurement oftriangles. Trigonometry is a branch of mathematics that developed from simplemeasurements.A theorem is the most important end in all of elementary mathematics. It wasthe motivation for a wealth of advanced mathematics, such as Fermats LastTheorem and the theory of Hilbert space. The Pythagorean Theorem asserts thatfor a right triangle, the square toes of the hypotenuse is equal to the sum of thesquares of the other two sides. There are many ways to prove the PythagoreanTheorem. A particularly simple one is the scale relationship for areas ofsimilar figures.Did Pythagoras derive the Pythagorean Theorem or did he piece it together bystudying superannuated cultures Egypt, Mesopotamia, India and China? What did theseancient cultures know almost the the orem? Where was the theorem used in theirsocieties? In "Geometry and Algebra in Ancient Civilizations", the authordiscusses who originally derived the Pythagorean Theorem. He quotes Proclos, acommentator of Euclids elements, "if we listen to those who wish to recount theancient history we may find some who refer this theorem to Pythagoras, and saythat he sacrificed an ox in awarding of his discovery". If this disputation isconsidered as a statement of fact, it is extremely improbable, for Pythagoraswas opposed to the sacrifice of animals, especially cattle. If the saying isconsidered as just a legend, it is easy to explain how such a legend might go forcome into existence. Perhaps the original form of the legend said somethinglike he who discovered the famous figure sacrificed a bull in honor of hisdiscovery.Van der Waerden goes on to comment that he believes the original discoverer wasa priest, before the time of Babylonian texts, who was allowed to sacrificeanim als and also was a mathematician. This question ordure never be answered, butevidence that societies used the theorem before the time of Pythagoras can befound.The Theorem is useful in everyday life. For example, at a certain(prenominal) time of day,the suns rays cast a three foot shadow off a four foot flag perch. Knowingthese two lengths, and the fact that the pole forms a ninety degree angle withthe ground, the distance from the end of the shadow to the top of the pole canbe found without measuring. The first step is to backup the given data