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Mathematics
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Apr 3, 2024
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Zahary Swain
Guided Essay #1
STEM185
The concept of deduction played a significant role in setting ancient Greek mathematics apart from ancient Egyptian mathematics. Deduction, as a logical method of reasoning, allowed the Greeks to develop a more rigorous and systematic approach to mathematics, which greatly influenced the development of Western mathematics. In contrast, ancient Egyptian mathematics relied more on practical applications and empirical observations (Bertoloni, 2006, p 43).
Ancient Egyptian mathematics, as explored in Jöran Friberg's book "Unexpected Links between Egyptian and Babylonian Mathematics", was primarily concerned with practical applications such as measuring land, building structures, and calculating volumes. The Egyptians
developed a system of arithmetic based on hieroglyphic numerals and used various mathematical
techniques to solve everyday problems. For example, the Rhind Mathematical Papyrus and the Moscow Mathematical Papyrus contain mathematical problems related to fractions, geometry, and algebraic equations (Friberg, 2015, p 144). However, the Egyptian approach to mathematics was more focused on finding practical solutions rather than developing abstract theories or proofs.
On the other hand, ancient Greek mathematics, as discussed in Friberg's book "Amazing Traces of a Bablonian Origin in Greek Mathematics", was characterized by a more deductive and
theoretical approach. Greek mathematicians, such as Euclid, Pythagoras, and Archimedes, sought to establish logical proofs and axiomatic systems to explain mathematical concepts. Euclid's "Elements" is a prime example of deductive reasoning in Greek mathematics. It presents
a systematic and rigorous treatment of geometry, starting from a set of axioms and using deductive reasoning to derive theorems and proofs (Friberg, 2015, p 145).
The Greeks also made significant contributions to algebra and number theory. For instance, Diophantus, introduced algebraic symbols and equations to solve problems involving unknown quantities (Friberg, 2015, p 145). This algebraic approach allowed for the development
of abstract mathematical concepts and the exploration of mathematical relationships beyond practical applications (Bertoloni, 2006, p 43).
The concept of deduction in Greek mathematics allowed for the establishment of logical frameworks and the development of abstract theories. This approach enabled Greek mathematicians to explore mathematical concepts in a more systematic and rigorous manner (Friberg, 2015). In contrast, ancient Egyptian mathematics focused more on practical applications and empirical observations, without the same emphasis on logical proofs and deductive reasoning (Bertoloni Meli, 2006).
In conclusion, the concept of deduction set ancient Greek mathematics apart from ancient
Egyptian mathematics. The Greeks' emphasis on logical proofs and deductive reasoning allowed for the development of abstract theories and systematic approaches to mathematics. In contrast, the Egyptians focused more on practical applications and empirical observations. The contributions of both civilizations have shaped the development of mathematics, but the deductive approach of the Greeks has had a lasting impact on Western mathematics.
Zahary Swain
Guided Essay #1
STEM185
Bertoloni, M. D. E. I., Dorn, H., & McClellan, J. E. I. (2006).
Science and technology in world history: An Introduction.
Johns Hopkins University Press.
Friberg (book author), J., & Sidoli (review author), N. (2015). Unexpected Links between Egyptian and Babylonian Mathematics and Amazing Traces of a Babylonian Origin in Greek Mathematics. Aestimatio
, 5
, 142–147. https://doi.org/10.33137/aestimatio.v5i0.25867
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