If only because in one’s “further” studies of mathematics, the results (i.e., theorems) of euclidean geometry appear only infrequently, this subject has come under frequent scrutiny, especially over the past 50 years, and at various stages, its very inclusion during a high-school mathematics curriculum has even been challenged. However, as long as we still think of important the event of logical, deduction in high-school students, then Euclidean geometry provides as capable a vehicle as any in bringing forth this worthy objective.
The lofty position ascribed to deductive reasoning goes back to at least the Greeks, with Aristotle having laid down the necessary foundations of such reasoning back in the 4th century B.C. At about this point, Greek geometry began to flourish and reached its zenith with the 13 books of Euclid. From now forward, geometry (and arithmetic) was an obligatory component of one’s education and served as a paradigm for the deduction.
A well-known (but not well enough known!) anecdote describes former U.S. president Lincoln who, as a member of Congress, had nearly mastered the primary six books of Euclid. By his own admission, this wasn’t a press release of any particular passion for geometry, but that such mastery gave him a decided edge over his counterparts is dialects and logical discourse.
Lincoln was not the only U.S. president to have given serious thought to Euclidean geometry. President Garfield published a completely unique proof in 1876 of the Pythagorean theorem.
As for the topic itself, it’s my personal feeling that the logical arguments which connect the varied theorems of geometry are equally as fascinating because of the theorems themselves!
Credits: David B. (Professor of Mathematics)
Related Pages : Geometry