Euclidean Geometry and Physical Space

David E. Rowe
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David E. Rowe: Johannes Gutenberg-Universität Mainz, Institut für Mathematik

Chapter 20 in A Richer Picture of Mathematics, 2018, pp 243-251 from Springer

Abstract: Abstract It takes a good deal of historical imagination to picture the kinds of debates that accompanied the slow process, which ultimately led to the acceptance of non-Euclidean geometries little more than a century ago. The difficulty stems mainly from our tendency to think of geometry as a branch of pure mathematics rather than as a science with deep empirical roots, the oldest natural science so to speak. For many of us, there is a natural tendency to think of geometry in idealized, Platonic terms. So to gain a sense of how late nineteenth-century authorities debated over the true geometry of physical space, it may help to remember the etymological roots of geometry: “geo” plus “metria” literally meant to measure the earth, of course. In fact, Herodotus reported that this was originally an Egyptian science; each spring the Egyptians had to re-measure the land after the Nile River flooded its banks altering the property lines. Among those engaged in this land surveying were the legendary Egyptian rope-stretchers, the “harpedonaptai” who were occasionally depicted in artwork relating to Egyptian ceremonials.

Date: 2018
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DOI: 10.1007/978-3-319-67819-1_20

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