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really. Is. Thales of Miletus. the. ?. Father of Greek Mathematics. Thales of Miletus. Born around 640 B.C.E.; died around 542 B.C.E. (dates differ, many sources say only that he lived about 600 B.C.E. Miletus is located in the modern country of Turkey. Ruins in Miletus. The Rumors.
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really Is Thales of Miletus the ? Father of Greek Mathematics
Thales of Miletus Born around 640 B.C.E.; died around 542 B.C.E. (dates differ, many sources say only that he lived about 600 B.C.E. Miletus is located in the modern country of Turkey. Ruins in Miletus
The Rumors *traveled to Egypt and brought back Egyptian geometry *predicted a solar eclipse (May 585 B.C.E.) *proved several geometric theorems *diverted a river to help an army cross *made a fortune by cornering the market of olive presses *was a political advisor *developed a method for determining the distance of ships at sea *measured the height of a pyramid *founded an Ionian school of natural philosophy *taught geometry to Anaximander *fell down a well while looking at the stars
Geometric Theorems attributed to Thales *a circle is bisected by its diameter *the base angles of an isosceles triangle are equal *when two lines intersect, vertically opposite angles are equal *the angle-angle-side congruence *the angle subtended by a diameter of a circle is a right angle Thales “discovered many propositions, and disclosed the underlying principles of many others to his successors, in case his method being more general, in others more empirical.” --Eudemus, via Proclus
The Witnesses None. No works written by Thales survive. No history about Thales that was written either during his lifetime or within 100 years of his life exists.
The Evidence Aristotle (about 260 years after Thales) -astronomer -made a fortune Proclus (Eudemus, 280 years after) (about 1050 years after Thales) -geometric proofs -history Diogenes Laertius (at least 800 years after Thales) Plutarch (about 690 years after Thales) Herodotus (about 150 years after Thales -engineer -astronomer -political advisor Plato (about 210 years after Thales -astronomer -falls in a well
Measuring the Pyramid *used concept of similar triangles (may have had knowledge of contents of Rhind Papyrus)0 *compared shadow of known object (like a person) with the pyramid shadow
The Spirit of the Times 600 B.C.E. to 300 B.C.E. *Greeks began to ask “Why?” -development of the proof -Euclid’s Elements (about 300 B.C.E.) *mathematics became a separate field of study *rational methods for science
The Verdict --We don’t know-- “There is no Proof!”
Bibliography Herodotus. The History of Herodotus. Great Books of the Western World, Vol. 6. Chicago: Encyclopeaedia Britannica, Inc., 1952. Plato. Theaetetus. Great Books of the Western World, Vol. 7. Chicago: Encyclopeaedia Britannica, Inc., 1952. Aristotle. Politics, Book 11. Great Books of the Western World, Vol. 9. Chicago: Encyclopeaedia Britannica, Inc., 1952. Katz, Victor J. A History of Mathematics: An Introduction, Second Edition. New York: Addison Wesley Longman, 1998. Struik, Dirk J. A Concise History of Mathematics, Fourth Revised Edition. New York, Dover Publications, 1987. Cuomo, Serafina. Ancient Mathematics. NewYork: Routledge, 2001. Diamandopoulous, P. The Encyclopedia of Philosophy, Vol. 7. New York: Macmillan Publishing Co., Inc. and The Free Press, 1967. Heath, Sir Thomas L. A Manual of Greek Mathematics. New York: Dover Publications, Inc., 1963. Anglin, W.S. and J. Lambek. The Heritage of Thales. Undergraduate Texts in Mathematics. New York: Springer-Verlag, 1995. Gow, James. A Short History of Greek Mathematics. New York, Chelsea Publishing Company, 1968. http://www-groups.mcs.st-andrews.ac.uk/Extras/Proclus_history_geometry.html Mac Tutor History of Mathematics/Additional Material Index/Proclus and the history of geometry as far as Euclid. Plutarch. The Lives of Noble Grecians and Romans. Great Books of the Western World, Vol. 14. Chicago: Encyclopeaedia Britannica, Inc., 1952. www.classicpersuasion.org/pw/diogenes/dlthales.htm Diogenes Laertius. The Lives and Opinions of Eminent Philosophers. London: Henry G. Bohn, 1853. Neyman, Jerzey and Niccolo Zucchi. Biographical Dictionary of Mathematicians, Vol. 4. New York: Simon & Schuster Macmillan, 1991. Young, Robyn V., editor. Notable Mathematicians: From Ancient Times to the Present. New York: Gale Research, 1997. Burnet, John. Early Greek Philosophy. http://faculty.evansville.edu/+62courses/phil211/burnet/ch1.htm Euclid. The Elements. Great Books of the Western World, Vol.11. Chicago: Encyclopeaedia Britannica, Inc., 1952.
The Problem of “Everyone Knows” You write in your diary, “I had cereal for breakfast this morning. I sure do love that Cap’n Crunch.” Fast forward 500 years. An archeologist finds your diary and reads the entry. How does the archeologist interpret the entry? *strolled out to a local field and picked cereal grains and ate them? *you did this in the company of a military officer with a funny name
The Problem of “Everyone Knows” What we know about that cereal that the future archeologist may not know: *the cereal was a processed product *the cereal contained non-cereal ingredients like sugar and preservatives *it came in a box or a bag *you bought it from a grocery store *you put it in a bowl *you poured milk over it *you ate it with a spoon *Cap’n Crunch is one of many varieties of cereal available Every culture makes assumptions about what “everyone knows.” The ancient Greeks are no exception.
