Moment 3: The Development of Inquiry
Up until 2600 years ago (recorded as 600 B.C. in Eves’s first book), geometry was dominated by finding angle congruency by cutting and measuring in a laboratory. But this method was not satisfactory to Greek Thales of Miletus; he wanted logic and reasoning not intuition and saws. Miletus wanted to prove congruency through deductive reasoning using axioms [4, page 64].
It may have been the Greeks’ interest in philosophy and inquiry, or the discovery of the necessary existence of irrational numbers [4, page 66], or that times were changing in Greece with the invention of an alphabet, moving from bronze to iron, the discovery of more far away lands on Earth or their love of art and beauty that drove the desire for a more advanced civilization. Humans appreciate beauty, as explained by Howard Eves in Great Moments in Mathematics Before 1650, page 18, on both an emotional level as well as an intellectual level. Whatever it was, the world was forever changed by this decision to make geometry more beautiful with logic rather than experiment.
Once the Greeks decided to go the deductive route, things really began to change in the fields of mathematics and art. The Greeks went on to deduct that there must be numbers on our number line that can not be expressed as fractions [4, page 44] when constructing a regular pentagon with rational sized angles and line segments [4, page 46-48]. The realization that inscribing a pentagon was not as easy as inscribing a triangle, square, or even a hexagon eventually led to the irrational [(1 + (sqrt(5))/2], or the “Golden Ratio”, that is now widely believed to infiltrate all of nature from flowers to nautilus shells to the architecture of the Parthenon to how we subconsciously measure physical beauty.
Works Cited:
[4] Eves, Howard, Great Moments in Mathematics Before 1650, The Mathematical Association of America, 1983
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