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arXiv · 2509.19361

Geometric Constructions through Ordered Sets

Liudmyla Morozova
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Abstract

This work develops an approach to geometric construction problems in which the given figure is regarded as an element of an ordered set generated by a construction process. Instead of seeking an isolated figure, the method constructs a chain in which each element follows logically from its predecessors. Three classical problems involving proportional segments, a Gothic detail, and proportional angles illustrate how the required solution emerges within such a structure. In the third problem, discrete links and a continuously varying radius form a two-parameter discrete-continuous structure. The examples also motivate a limited interpretation of information conservation within an ordered construction.

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Liudmyla Morozova. 2026-08-16. Geometric Constructions through Ordered Sets. https://arxiv.org/abs/2509.19361

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