Geometry

2504 Submissions

[4] viXra:2504.0201 [pdf] submitted on 2025-04-30 21:53:51

Drawing Bent to Straight a New Solution to Geometric Problems

Authors: Hongfa Zi, Lei Zi
Comments: 6 Pages.

This article proposes an innovative method based on geometric transformation and limit construction, which successfully solves the problem of "drawing curves as straight". By introducing a linear function of fixed arc length and isosceles trapezoid, we prove that the transformation between a circle and an equal area square can achieve geometric equivalence in finite steps, and provide specific graphical steps and mathematical proof. This study reveals the limitations of traditional ruler drawing constraints and achieves accurate area conversion through an extended toolkit. Finally, the paper discusses the mathematical significance of this solution, including the algebraic treatment of the transcendental number and its supplementation to the Euclidean geometry system.
Category: Geometry

[3] viXra:2504.0151 [pdf] submitted on 2025-04-24 20:47:51

A Refined Symmetric Mean Integral Approach to Bounding the Perimeter of an Ellipse

Authors: Harun Abdul Rohman
Comments: 6 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

We refine the symmetric mean integral method for estimating the perimeter of an ellipse by restricting the integration limits to [0,π/4]. This approach allows the application of the squeeze theorem by leveraging the extremal behavior of the integrand, yielding explicit upper and lower bounds. The results provide a foundation for further research to derive improved perimeter estimates for ellipses.
Category: Geometry

[2] viXra:2504.0063 [pdf] submitted on 2025-04-09 10:52:09

Integrabily And Cohomology And 6-Sphere

Authors: Jun Ling
Comments: 6 Pages.

We construct a differential from Nijenhuis tensor of any almost complex structure on a differentiable manifold, and show a relationship between the integrability of the almost complex structure and the cohomology of the manifold. For the case of 6-sphere, we first show that this form does not vanish for a special almost complex structure, and then show that this form does not vanish for any almost complex structure on the 6-sphere. Therefore all almost complex structures on 6-sphere are not integrable.
Category: Geometry

[1] viXra:2504.0039 [pdf] replaced on 2025-06-01 12:24:42

Translation of the Kimberling's Glossary Into Barycentrics ("le Glossaire de Pierre")

Authors: Pierre L. Douillet
Comments: 521 Pages.

Described at https://faculty.evansville.edu/ck6/encyclopedia/ETC.html by "if you're unsure of a term, click Glossary or Pierre Douillet's much expanded and very useful version".
Category: Geometry