Thales of Miletus: (A Brief History)
(624 BC – 547 BC)

Thales of Miletus appears to be the first great Greek mathematician; however, his occupation was actually an engineer. As mentioned before, none of the original writing has survived, so his exact views and mathematical discoveries are not completely certain. There is some evidence suggesting that he wrote a book on navigation in which he defined the constellation Ursa Minor.

Many have tried to account for how Thales measured the height of pyramids. One account states that he did this “by observation of the length of their shadow at the moment when our shadows are equal to our own height.” This does not suggest any geometric ideas, however a later account suggests that he was getting close to the concept of similar triangles: “…[He] merely set up a stick at the extremity of the shadow cast by the pyramid and, having thus made two triangles by the impact of the sun’s rays, … showed that the pyramid has to the stick the same ratio which the shadow [of the pyramid] has to the shadow [of the stick]. It is quite possible that he did incorporate this geometrical idea to solve practical problems without even realizing what he was doing geometrically.

Others argue, however, that he knew exactly what he was doing and was well aware of the meaning of a geometric proof. There are many textbooks on the history of geometry that accredit him to five theorems:

i. A circle is bisected by any diameter.
ii. The base angles of an isosceles triangle are equal.
iii. The angles between two intersecting straight lines are equal.
iv. Two triangles are congruent if they have two angles and one side equal.
v. An angle in a semicircle is a right angle.

Theorem (iv) is said to have been used by Thales to calculate the distance of ships from the shore. One account of how he may have calculated this is by first nailing an instrument consisting of two sticks into a cross so that they could be rotated around the nail. Next, on top of a tower, he would have positioned one stick vertically and rotating the other until it pointed at the ship. Finally, he would rotate this instrument until the moveable stick points at the wanted point on the land. The distance of this point from the base of the tower equals the distance to the ship.

There is much conflict on what Thales of Miletus is really responsible for. Regardless, he is known to be the first Greek mathematician, so he must have had a good grip on geometrical concepts.

References:

Development and History. 3rd ed. New York: W.H. Freeman and Company,
1993. 6-19.

National Council of Teachers of Mathematics, 1969.