Jake Peppiatt
Ellsworth High School
Calculus Class
December 2001
Tales of Thales
Thales was a rich merchant from Miletus in Greece, living from about 640 B.C. to 550 B.C. As a merchant he traveled to many cities of the ancient world, and his natural intelligence allowed him to learn much from the people he met. After his death, he became known as one of the Seven Sages of Greece, and many stories were attributed to him.
Once, it was said, he was leading mules that were carrying sacks of salt. At one river crossing a mule fell in the water, dissolving his salt, and thus, significantly lightening his load. At the next crossing, the mule purposely submerged his burden of salt and again was relieved of his cargo. To correct this, Thales filled a sack with natural sponges, and when the mule dipped at the third crossing, the sponges absorbed water and became much heavier than even the salt would have been. This fixed the problem.
Another time, foreseeing an exceptionally good olive crop, Thales gained ownership of all the olive presses he could and became master of the market. However, he didn't exploit the customers. Proving what he could do was enough for him, and he sold the olives at a reasonable price.
A third story involves his love for astronomy (he once successfully predicted a solar eclipse in 585 B.C.). It goes that Thales was on an evening walk, in deep concentration on the heavens and he fell into a ditch. An old woman who saw hem remarked, "How canst thou know what is doing in the heavens when thou seest not what is at thy feet?"
Many mathematical discoveries that we take for granted are attributed to Thales. He is said to have proved that a circle is bisected by any diameter, that the angels at the base of an isosceles triangle are equal, the angle in a semicircle is a right angle, and the sides about equal angles in similar triangles are proportional.
The Egyptian priests Thales visited on his travels as a merchant influenced most of these discoveries. Early Egyptians were master of practical geometry. For proof of this, one needs look no further than the pyramids at Cairo, which show much similarity with a regular pentagon. In fact, the area of each triangular face of the Great Pyramid is equal to the square of its height. Thales actually determined the height of the Great Pyramid by comparing its shadow on the ground to the shadow of a vertical stick, thus using his knowledge of equal ratios or proportions.
Some of the practical achievements given by Thales to man were the discovery of the correct number of days in a year and a way, involving trigonometry, not unlike his measuring of the Great Pyramid, to find the distance of a ship observed at sea.
In closing, I must say that I was very impressed with the discoveries of Thales in such a bygone time when so little was known about the world around us. It must have been very frustrating and time-consuming work, and this causes one to feel quite insignificant when he or she can't even complete a simple Calculus assignment when all the really difficult work was done by men such as Thales.
Great Mathematicians, The Newman, James R. Methuen and Company, LTD. London England. 1929.