Abstract
The word geometry literally means earth measurement. When geometry was developed by the ancients of various cultures, it was probably for earth measurement, that is, surveying. In mathematics today, geometry generally refers to the study of curves and surfaces. Different branches of geometry—differential geometry, algebraic geometry, geometric analysis—are distinguished in part by the objects of study and in part by the different sets of tools brought to bear upon the objects of study. In differential geometry, for example, the objects are curves and surfaces in complex space and the tools arise largely from differential calculus. Algebraic geometry is the study of objects that can be described using rational functions and the tools arise typically, but not always, from modern algebra.
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- 1.
Pause to ponder the timeframe: Euclid and Proclus were approximately 750 years apart, while Shakespeare and we are approximately 400 years apart.
- 2.
There is a legend that Ptolemy , a king of Egypt, asked Euclid , his tutor, if there was not a shorter way to learn geometry. Must one go through The Elements? Euclid’s response was that there was “no royal road to geometry.” Similar stories are attributed to other mathematicians in response to complaints from other kings trying to learn mathematics. See [7], p. 1.
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Alexandria is named for Alexander the Great, who, as a child, studied with Aristotle.
- 4.
This is the origin of the word academic. Academy is actually the name of the place where Plato set up his institution. The Academy remained in use until 526, another astonishingly long-lived force in the intellectual world.
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Dillon, M.I. (2018). The Elements of Euclid. In: Geometry Through History. Springer, Cham. https://doi.org/10.1007/978-3-319-74135-2_1
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DOI: https://doi.org/10.1007/978-3-319-74135-2_1
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