The arithmetic of solids

Details The arithmetic of solids The arithmetic of solids

2012-04-06

arxiv.org/abs/1204.2219v1

Mathematics

General Mathematics

31 pages, 29 figures

Scientific paper

The set of segments, each of the next is n times bigger than the first one is a simple geometric interpretation of the set $\mathbb{N}$ of natural numbers. In this paper we investigate the opposite situation. We construct an algebraic structure similar to the set $\mathbb{N}$ which describes the set of congruent triangles, each of the next has the sides n times bigger than the first one. Later we do the same with the set of congruent tetrahedrons, and finally with a set of simplices of any dimension.

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