Several ancient Greek philosophers and mathematicians over many centuries considered and analyzed ideas akin to dimension. They grappled with basic concepts and implicit theories that touch on dimension. They put forward and examined fundamental ideas related to the dimension concept as embodied in the four basic geometrical figures of point, line, surface, and solid, their hierarchical ordering, and their mutual relations. From a modern point of view these figures are low-dimensional objects, i.e., objects of 0, 1, 2, and 3 dimensions, though the ancient Greek thinkers would not have identified them in this way.

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Ideas Touching on Dimension in Ancient Greek Philosophy and Mathematics

  • Dale Martin Johnson

摘要

Several ancient Greek philosophers and mathematicians over many centuries considered and analyzed ideas akin to dimension. They grappled with basic concepts and implicit theories that touch on dimension. They put forward and examined fundamental ideas related to the dimension concept as embodied in the four basic geometrical figures of point, line, surface, and solid, their hierarchical ordering, and their mutual relations. From a modern point of view these figures are low-dimensional objects, i.e., objects of 0, 1, 2, and 3 dimensions, though the ancient Greek thinkers would not have identified them in this way.