TL;DR
This paper presents a new, simplified proof of Dehn's theorem by extending the concept of area and translating additive functions into elementary mathematics language.
Contribution
It introduces a novel approach to prove Dehn's theorem through a generalized notion of area and additive functions.
Findings
Simplified proof of Dehn's theorem
Generalization of area concept
Method translation into elementary math language
Abstract
We give a new simple proof of Dehn's theorem by generalizing the notion of area. The method proposed in the present article is actually the "translation" of the method of additive functions into the elementary math language.
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Taxonomy
TopicsMathematics and Applications · semigroups and automata theory · Functional Equations Stability Results