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[3] viXra:2506.0107 [pdf] submitted on 2025-06-19 20:53:19
Authors: Andrey V. Voron
Comments: 14 Pages.
Two variants of the geometry of the Durer polyhedron, conventionally named as "traditional" and "alternative", are investigated. The geometric properties of both variants of polyhedra are revealed. According to the results of the field experiment, it was revealed that the "alternative" version of the polyhedron has the property of complementarity.
Category: Geometry
[2] viXra:2506.0046 [pdf] submitted on 2025-06-10 10:45:51
Authors: Binyin Zheng
Comments: 27 Pages.
This paper proposes and systematically elaborates a novel geometric framework—non-differential geometry—whose core lies in entirely abandoning the reliance on smoothness ($C^1$ or higher continuity) required by traditional differential geometry, demanding only $C^0$ continuity for geometric objects. By introducing new mathematical tools based on limits and infinite series, non-differential geometry overcomes the smoothness constraints in calculating geometric quantities such as curvature. Furthermore, this paper constructs a unique ``integration tool" (distinct from classical integration theory) specific to non-differential geometry, providing a novel approach for analyzing geometric objects. Current research focuses on Euclidean space, but the theoretical framework itself is not confined to any specific spatial structure and is applicable across low- to high-dimensional spaces. Non-differential geometry completely resolves the contradiction between continuity and differentiability and offers potential support for theoretical innovations in fields such as physics.
Category: Geometry
[1] viXra:2506.0029 [pdf] replaced on 2026-04-29 21:21:47
Authors: Rolando Zucchini
Comments: 7 Pages.
This type of cubic curve, in the United Kingdom known as the Witch of Agnesi, it is approached from a geometric, trigonometric and analytical point of view; using the scheme: model, algorithm, resolution, graph.
Category: Geometry
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