How is it that the Greeks managed to advance their mathematical knowledge to the point that it became superior to the Egyptians, a civilization far older? As early as 3500 BCE Egyptian (and also Babylonian) calculations were the finest in the world. Egyptians used their mathematical knowledge largely for engineering purposes; without it, building the great pyramids and other breathtaking monuments would have been impossible.
What the Greeks derived from Egyptian mathematics were mainly rules of thumb with specific applications. Egyptians knew, for example, that a triangle whose sides are in a 3:4:5 ratio is a right triangle. This was because in order to form right angles, the practical minded Egyptian land surveyors used a rope divided into twelve equal parts, forming a triangle with three parts on one side, four parts on the second side, and five parts on the remaining side. The right angle was to be found where the …show more content…
The technique of generalization, which is about developing general principles with broad applications, rather than rules with specific use. The theorem developed by Pythagoras was true not only for the 3:4:5 triangle, but it was a principle applicable to any other right triangle, regardless of its dimensions. Furthermore, the theorem showed that a triangle is a right triangle if, and only if, the square of the longest side matches the sum of the squares of the remaining two sides: the right angle lay where the two shorter sides met.
3. The art of deductive reasoning. This is about having a set of initial general statements or premises and reaching conclusions by working out its logical implications.
4. Mathematics in the sense of demonstrative deductive arguments. By combining deductive reasoning and generalization, mathematics was no longer seen as a static set of rules but rather as a dynamic system capable of complex development.
5. We owe to Pythagoras, or maybe to his followers, these important Greek innovations in the field of