Ancient Egyptian Mathematics

Abstract: This paper is a report about the ancient Egyptians mathematics. The report discusses the unique counting system and notation of the ancient Egyptians, and their hieroglyphics. One of the unique aspects of the mathematics is the usage of “base fractions”. The arithmetic of the Egyptians is also discussed, and how it compares to our current methods of arithmetic. Finally, the geometrical ideas possessed by the Egyptians are discussed, as well as how they used those ideas.

Introduction

One of the first, large steps in the evolution of mathematics took place in Egypt and Babylon, around 2000 BCE. (Egyptian Mathematics, n.d.) During this period, mathematics started evolving from only basic counting, to mathematics that is more

They needed arithmetic for the complex calculations used in creating the architectural wonders, as well as algebra to help solve logistical problems such as keeping the population fed. Ancient Egyptians could perform addition and subtraction using grouping, but for multiplication and division, had more complex methods. These methods for multiplication and division are basically binary operations.

For the multiplication of two numbers, the method is as follows: two columns of numbers were created, one column is the powers of two, and the other column is one of the numbers being multiplied, consistently doubled. Then, by splitting up the second number as the sum of powers of two, and using the laws of distribution and the columns, find the answer (Egyptian Mathematics, n.d.). An example follows:

Consider 43×38. First, the right column will be the powers of two, and the left column will be 43, constantly doubled (this can be achieved by basic addition). The red columns are just to aid the explanation.

43×1 43

They knew the general formula for the volume of a square based pyramidal frustum, V=1/3 h(b_1^2+b_1 b_2+b_2^2 ), where h is the height, b_1 is the side length of the base, and b_2 is the side length of the top square. They also knew the formula for the volume of a square based pyramid, by setting the side length of the top square equal to 0, getting V=1/3 hb_1^2. An interesting note is that to prove the formula for the pyramid, knowledge of calculus, and specifically an idea of continuity is required, meaning the Egyptians had no proof of this formula. (Weisstein, n.d.) This may come to no surprise though, as most of the Egyptians mathematics was based on practicality and applications, instead of generalizations and proofs. This would explain why they mistakenly used incorrect formula for quadrilaterals. They may have been able to find the volume of a pyramid, in a similar way we may have done in elementary school: by building the shapes out of sand. Egyptians may have created a square-based pyramid out of wet, packed sand, using basic tools (for example, creating a cube, and then shaving off edges to create the pyramid). Then, they could move the sand into a cube shaped box, where the box had the same base dimensions as the pyramid. Then, by flattening the sand, one could notice the sand would fill the cube one third of the way up. (Pyramid Sand,