Sunday, March 24, 2019

Trigonometry :: essays research papers

TrigonometryTrigonometry uses the detail that ratios of pairs of sides of triangles arefunctions of the angles. The basis for mensuration of triangles is the right-angled triangle. The term trigonometry center liter totallyy the measurement oftriangles. Trigonometry is a branch of mathematics that essential from simplemeasurements.A theorem is the most important result 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 of the hypotenuse is jibe to the sum of thesquares of the other two sides. There are many ways to prove the PythagoreanTheorem. A particularly simple one is the grading relationship for areas ofsimilar figures.Did Pythagoras derive the Pythagorean Theorem or did he component it together bystudying ancient cultures Egypt, Mesopotamia, India and China? What did theseancient cultures agnize ab out the theorem? Where was the theorem used in theirsocieties? In "Geometry and Algebra in Ancient Civilizations", the authordiscusses who trustworthyly derived the Pythagorean Theorem. He quotes Proclos, acommentator of Euclids elements, "if we listen to those who propensity to recount theancient history we may find some who relate this theorem to Pythagoras, and saythat he sacrificed an ox in honor of his discovery". If this rehearsal isconsidered as a statement of feature, it is extremely improbable, for Pythagoraswas opposed to the sacrifice of animals, oddly cattle. If the saying isconsidered as just a leg intercept, it is easy to explain how such a legend might havecome into existence. Perhaps the original form of the legend said somethinglike he who discovered the celebrated 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 metre of Babylonian texts, wh o was allowed to sacrificeanimals and also was a mathematician. This question stinker neer 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 trustworthy time of day,the suns rays cast a three foot shadow dispatch a four foot flag pole. 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 maiden step is to substitute the given data

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