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Compare geometry in Ancient Egypt and Mesopotamia
February 14, 2019
1 Introduction
Geometry is the branch of mathematics concerned with the properties and relations of points, lines, surfaces, solids,
and higher dimensional objects [1]. Geometric concepts were being utilised as early as 3000 BCE by the Egyptians
and Babylonians, it was a beneficial approach to enhance social well being of the civilisations such as tax collection,
building, trade and other practises [2]. Some important Egyptian documents were written in hieratic script; Rhind
Papyrus (1650 BCE) and Moscow Papyrus (1800 BCE), which were well preserved in the dry climate. However,
collecting Mesopotamia information has been more challenging as mathematical data was stored on small clay
tablets in cuneiform script. Consequently, intellects have dedicated their research to creating a mosaic picture out
of a collection of dispersed tablets to solve particular problems [8][pg:34-35]. Both civilisations pioneered a broad
basis of geometry with different approaches, including calculating the area and volume of shapes, and applied these
techniques in practical scenarios such as astrology and constructing the pyramids [2].
2 Pythagorean Theorem
Formally, one of the most renowned statements in geometry is the Pythagorean Theorem and is defined in terms of
area: “In any right triangle, the area of the square whose side is the hypotenuse is equal to the sum of the areas of the
squares whose sides are the two legs”. This is translated to define a formula characterizing the Pythagorean triples
[5]. It has been found that both regions illustrated knowledge of Pythagoras’s theorem by different interpretations
of the proposition.
To begin, it was certain that the Babylonians knew of Pythagoras’ theorem as 4 tablets demonstrated distinct
connections [4], One specific example was reserved on the YBC 7289 tablet, dating back to 1800-1600 BCE. From
figure 1, the translation explains that the number along the upper left side is 30 and the number under the horizontal
diagonal written in modern notation as 1; 24, 51, 10 is 1 + (24/60) + (51)/(60)2 + (10)/(60)3 = 1.414213, also known
as
√
2 to the nearest one hundredth thousand. We then find that d = 30 · (2) = 42; 25, 35 [5]. The relationship of
a triangles diagonal and its sides is clear, with the hypotenuse equaling
√
2 and each side equaling 1, illustrating
convincing evidence of Pythagorus’ theorem [7].
Figure 1: An illustration of the original tablet YBC 7289, with dialogue written in the Babylonian number system
and the modern interpretation on the right hand side. [7]
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Whereas, it has been noted that the Egyptians laid out right angles by sketching a rope with 12 equal intervals
knotted on it, to form a 3-4-5 triangle: a renowned Pythagorean triple [8]. The first-century polymath Plutarch
conducted the following hypothesis that “the Egyptians regarded one triangle above all the others as 3 is the first
odd and perfect number, 4 is the squ...
