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## Ancient Greek and Egyptian Mathematics

Greek mathematicians were more focused on the practical application of mathematical concepts. A detailed analysis of the derived concepts was lacking in Ancient Egyptian mathematics. The approach adopted in Egypt failed to recognize flexibility. For example, mathematicians in Egypt focused on rigid mathematical rules to analyze particular objects. Egyptian mathematicians claimed that any triangle with sides in a 3:4:5 ratio is a right triangle (Violatti). There is no clear record of how Egyptians developed this mathematical concept. In addition, the formula lacked further analysis to help scientists examine its validity and specify its applicability to the different areas.

The deduction concept by the Greek mathematicians questioned the validity and applicability of the concepts developed by the Egyptian mathematicians. Greek mathematicians were more focused on the logical limits of documented mathematical concepts. For example, scientists focused on stretching the 3:4:5 triangle idea to make it flexible and applicable to various areas (Violatti). Greek scientists’ deductive reasoning was also focused on geometric objects instead of numbers. The primary aim of the Greek mathematicians was to ensure people could apply mathematical concepts to different areas provided that the concepts guaranteed valid results. In addition, Greek mathematicians emphasized mathematical concepts that could be applied universally to every situation.

The technique of abstraction was more critical to Greek mathematicians. The concepts developed by Ancient Greece’s scientists aimed to promote the quality of dealing with ideas rather than events. The concept of deduction was crucial to ensuring that mathematical concepts were not limited to physical considerations (Violatti). For example, in the case of the triangle, Greek mathematics focuses on the property of a straight line instead of the physical appearances of the objects under analysis.

The deductive concepts by Greek mathematicians consider the fundamental elements and disregard the non-essential ones. This approach differed from Egyptian mathematical concepts that focused on physical objects and disregarded the fundamental ones (Violatti). Egyptian mathematical principles considered mathematics a static subject with static rules. The deductive concept of Greek mathematics combined reasoning and generalization. Greek mathematicians valued the approach to deriving conclusions by working on the logical implication of the concepts. The Pythagorean theorem is, for example, a concept scientists could apply to any right triangle. The deductive concepts ensured that people did not have to worry about the triangle dimensions when applying Pythagoras’ theorem.

Egypt’s ancient civilization’s counting system was decimal. The principle allowed scientists to deal with numbers on a large scale. However, the concepts did not have a precise method to construct a number arbitrarily large. The other mathematical principle in ancient Egypt is rounding up numbers. Scientists, for example, used the fraction of 7/5 to determine the square root of 2 (Violatti). This approach, however, allowed room for mathematical errors, as noted by the Greek mathematicians.

Greece’s mathematicians developed strict principles that focused on the exactness of the mathematical figures. Greece’s principles emphasized that rounding off was insufficient, and there was a need to adhere to mathematical rigor. The Greek mathematical concepts apply to the different parameters. According to Greek mathematical principles, a triangle with two angles and one side equal to another triangle possesses similar properties in all other aspects (Page). In addition, an isosceles triangle has all the angles at the base equal.

Although there are significant differences between Ancient Greek and Egyptian mathematics, Greek mathematicians borrowed some concepts from Egyptian scientists. Much of the study carried out by Greek mathematics provides an improved and detailed analysis of what the Egyptian mathematicians focused on in the subject. The deduction concept in ancient Greek forms the basis for the differentiation between the two civilizations. For example, Egyptians focused more on physical properties, while Greek scientists emphasize reasoning and generalization. The deduction concept is the primary reason for the differences in the mathematical principles between the two civilizations.

## Works Cited

Page, John. “Thales of Miletus—A Short Biography.” OpenStax, https://cnx.org/contents/qvnC-NGP@1/Thales-of-Miletus-a-short-biography. Accessed 24 October 2022.

Violatti, Cristian. “Greek Mathematics.” World History Encyclopedia, www.worldhistory.org/article/606/greek-mathematics. Accessed 24 October 2022.