History and Culture: Essay 1

Essay title: Outline the range of problems in algebra and geometry considered by either the ancient Egyptians or the ancient Babylonians, indicating the techniques they used to solve them.

The Egyptian civilisation is a precursor in the mathematical reflexion. The use of this scientific tool was a support to their daily tasks, such as the construction of habitats or the wage distribution. A practical utilization can be seen throughout the range of problems they faced, outlined here below. In both algebra and geometry, the Egyptians have demonstrated very interesting techniques to solve their puzzles.

One of the most admirable work was certainly its calculus of fractions. They were mainly expressed in the 1n form (23 and 34 being the exceptions), called unit fractions. The choice of unit fractions could be motivated by a will for equal distribution. In the Rhind papyrus, one of the rare vestige of the Egyptian mathematical work, Ahmes, the author, tries to divide 9 loaves equally among 10 men. Instead of taking a tenth off to every loaf, leaving the last man with crumbs, the Egyptians would use the decomposition of 2n fractions into a sum of unit fraction table. Each men would then get 910=12+13+115.

The Egyptians were the very first to solve “aha problems”, a primitive form of linear equation. The false position method was the most common technique employed. By setting a convenient and incorrect answer, and by adjusting it using proportionality, they could solve the following problem: “A quantity and its 17 added together become 19. What is the quantity?” Here, the convenient answer is 7. The left-hand side total is 8. By proportionality, we multiply the answer 7 by 198=2+14+18. The answer is therefore 16+12+18. They showed evident knowledge in proportion of two quantities.

The Egyptians were able to estimate surface areas, very useful for land taxation. In geometry, their major feat is their pi approximation.