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In this chapter I shall examine the development of theories of higher-dimensional spaces, that is, spaces beyond 3 dimensions to 𝑛 or infinite dimensions, that occurred during the nineteenth century. Early in the century there were mathematical forays into the world of higher-dimensional spaces, with Gauss being a principal explorer. The main development of such theories then took off in the 1840s, 1850s, and 1860s with the publication in rapid succession of works by Grassmann, Cayley, Riemann, and several others.

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Nineteenth-Century Theories of Higher-Dimensional Spaces

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  • 发表日期：

    2025年

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  • Dale Martin Johnson

摘要

In this chapter I shall examine the development of theories of higher-dimensional spaces, that is, spaces beyond 3 dimensions to 𝑛 or infinite dimensions, that occurred during the nineteenth century. Early in the century there were mathematical forays into the world of higher-dimensional spaces, with Gauss being a principal explorer. The main development of such theories then took off in the 1840s, 1850s, and 1860s with the publication in rapid succession of works by Grassmann, Cayley, Riemann, and several others.