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[3] viXra:2601.0085 [pdf] submitted on 2026-01-21 23:21:49
Authors: Harish Chandra Rajpoot
Comments: 14 Pages. (Note by viXra Admin: Please don't name a theorem/formula/equation etc after the author's name)
In this paper, a theorem is formulated and proved that yields generalized closed-form expressions for the dihedral angle between any two arbitrary lateral faces of a regular n-gonal right pyramid. The dihedral angles are expressed in terms of the apex angle, defined as the angle between two adjacent lateral edges meeting at the apex. The proposed formulation establishes a direct analytical relationship between the edge geometry at the apex and the corresponding dihedral angles of the pyramid. Due to its generality, the theorem applies to all regular and uniform polyhedra whose vertex configuration coincides with that of a right pyramid, as well as to regular n-gonal right prisms with an arbitrary number of sides. The resulting formulas are useful for geometric modeling, construction of physical models, and the development of computational algorithms for the analysis of polyhedral structures and equally inclined sets of concurrent vectors in three-dimensional space.
Category: Geometry
[2] viXra:2601.0080 [pdf] replaced on 2026-02-17 00:55:16
Authors: Bin Wang
Comments: 15 Pages.
We show that on a complex projective manifold $X$, for $mathbb G=mathbb R$ or $mathbb Q$, a class in $H^{p, p}(X;mathbb Z)otimes mathbb G$ is represented by a convergent infinite series of integration currents over algebraic cycles with real coefficients. It implies that a Hodge class is represented by an algebraic cycle with rational coefficients.
Category: Geometry
[1] viXra:2601.0063 [pdf] submitted on 2026-01-16 02:59:56
Authors: Erkan Gürkan
Comments: 6 Pages.
This study positions the ellipse not merely as a static definition, but as the embodiment of a dialogue between perception and mathematics, a living expression of balance. Through a poetic-philosophical narrative, the (F1 and F2) foci are revealed as symbols of complementary opposites, approaching and separating in a continuous act of creation. The research demonstrates that the ellipse functions not only as a static locus of points but as a self-regulating, dynamic structure governed by an "Internal Law of Balance" and a "Four-Quarter Mathematical Repetition Program." This structure manifests as a continuous unit value exchange between the axes, analytically detailing how the ellipse is cyclically regenerated across four symmetrical quarters. This approach expands the current understanding of the ellipse, positioning it not merely as a defined curve, but as a structure that reveals an intrinsic and continuous mathematical process that necessitates radical revisions in the field of geometry.
Category: Geometry
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