Term Papers on Trigonometry

Term Paper Title	Trigonometry
# of Words	501
# of Pages (250 words per page double spaced)	2

Trigonometry

Trigonometry uses the fact that ratios of pairs of sides of triangles are
functions of the angles.  The basis for mensuration of triangles is the right-
angled triangle.  The term trigonometry means literally the measurement of
triangles.  Trigonometry is a branch of mathematics that developed from simple
measurements.

A theorem is the most important result in all of elementary mathematics.  It was
the motivation for a wealth of advanced mathematics, such as Fermat's Last
Theorem and the theory of Hilbert space.  The Pythagorean Theorem asserts that
for a right triangle, the square of the hypotenuse is equal to the sum of the
squares of the other two sides. There are many ways to prove the Pythagorean
Theorem.  A particularly simple one is the scaling relationship for areas of
similar figures.

Did Pythagoras derive the Pythagorean Theorem or did he piece it together by
studying ancient cultures; Egypt, Mesopotamia, India and China?  What did these
ancient cultures know about the theorem?  Where was the theorem used in their
societies?  In "Geometry and Algebra  in Ancient Civilizations", the author
discusses  who originally derived the Pythagorean Theorem.  He quotes Proclos, a
commentator of Euclid's elements, "if we listen to those who wish to recount the
ancient history we may find some who refer this theorem to Pythagoras, and say
that he sacrificed an ox in honor of his discovery".  If this statement is
considered as a statement of fact, it is extremely improbable, for Pythagoras
was opposed to the sacrifice of animals, especially cattle.  If the saying is
considered as just a legend...

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