Ancient Greek Research Paper

As the Greek empire began to spread its sphere of influence into Asia Minor, Mesopotamia and beyond, the Greeks were smart enough to adopt and adapt useful elements from the societies they conquered. This was as true of their mathematics as anything else, and they adopted elements of mathematics from both the Babylonians and the Egyptians. But they soon started to make important contributions in their own right and, for the first time, we can acknowledge contributions by individuals. By the Hellenistic period, the Greeks had presided over one of the most dramatic and important revolutions in mathematical thought of all time.

The ancient Greek numeral system, known as Attic or Herodianic numerals, was fully developed by about 450 BCE, and in

Thales, one of the Seven Sages of Ancient Greece, who lived on the Ionian coast of Asian Minor in the first half of the 6th Century BCE, is usually considered to have been the first to lay down guidelines for the abstract development of geometry, although what we know of his work (such as on similar and right triangles) now seems quite elementary.

Thales established what has become known as Thales' Theorem, whereby if a triangle is drawn within a circle with the long side as a diameter of the circle, then the opposite angle will always be a right angle (as well as some other related properties derived from this). He is also credited with another theorem, also known as Thales' Theorem or the Intercept Theorem, about the ratios of the line segments that are created if two intersecting lines are intercepted by a pair of parallels (and, by extension, the ratios of the sides of similar

These intransigent problems were profoundly influential on future geometry and led to many fruitful discoveries, although their actual solutions (or, as it turned out, the proofs of their impossibility) had to wait until the 19th Century.

Hippocrates of Chios (not to be confused with the great Greek physician Hippocrates of Kos) was one such Greek mathematician who applied himself to these problems during the 5th Century BCE (his contribution to the “squaring the circle” problem is known as the Lune of Hippocrates). His influential book “The Elements”, dating to around 440 BCE, was the first compilation of the elements of geometry, and his work was an important source for Euclid's later work.

Zeno's Paradox of Achilles and the