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[3] viXra:2509.0136 [pdf] submitted on 2025-09-25 20:48:12
Authors: Roberto C. M. Navacchia
Comments: 8 Pages. In Portuguese; License: CC BY-NC (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
This paper presents an alternative method of analysis for identifying pulsars using data from the High Time Resolution Universe Survey neutron star catalog and the construction of radial curves derived from statistical parameters of the observed radio signals, where, through a geometric approach, highlights their unique and distinct signature for each pulsar, which differs significantly from the curves produced by noise signals. The method seeks to offer the scientific community a complementary means of classification, opening up possibilities for the creation of a ‘Geometric Atlas of Pulsars’ useful in Astrophysics, Data Science, Quantum Mechanics, and especially in Analytical Geometry.
Category: Geometry
[2] viXra:2509.0119 [pdf] submitted on 2025-09-20 19:47:56
Authors: Florian Gashi
Comments: 4 Pages. (Note by viXra Admin: Please cite and list scientific references)
In this work, a precise characterization is given of those perspective affine reflections that preserve both the arc length and the magnitude of curvature for any smooth planar curve. The result shows that the only non-trivial transformation with this property is the orthogonal reflectionwith respect to the given axis, i.e., the perpendicular affine symmetry with characteristic constant k=-1.
Category: Geometry
[1] viXra:2509.0057 [pdf] submitted on 2025-09-10 17:17:49
Authors: Sigrid M. -L. Obenland
Comments: 6 Pages.
As is generally known, the side of a cube having twice the volume of a cube with volume 1 is 2^(1/3). It has been proven to be impossible to construct the cube having twice the volume of the initial cube with compass and straightedge (ruler) alone, when starting with a cube of 1 unit. The ancient Greeks devised several methods by using additional tools1, and later Albrecht Dürer has found a method of constructing the ratio of 1 to 2^(1/3) by a method wherein two sections of a certain straight line have to be made of equal length by trial and error2. I here present a simple new method of constructing the ratio of 1 to 2^(1/3) that uses a compass, a straightedge and properties of a normal parabola that can be drawn with compass and straightedge by tackling the problem in reverse order, i.e. starting from a cube having a side length of 2^(1/3) in an arbitrary system of units and, thus, a volume of 2 in the same system, and constructing the side length of a cube with half the volume in the arbitrary system of units. By using the intercept theorem this can be converted to any desired unit, such as cm. It should be noted that a length unit as displayed on the screen, such as 1 cm, may not be preserved when this document is printed on paper.
Category: Geometry
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