Geometry

1802 Submissions

[8] viXra:1802.0196 [pdf] replaced on 2018-02-16 15:58:29

A Note on a Problem Invoving a Square in a Curvilinear Triangle

Authors: Hiroshi Okumura
Comments: 3 Pages. The paper is considering a problem in Wasan geometry.

A problem involving a square in the curvilinear triangle made by two touching congruent circles and their common tangent is generalized.
Category: Geometry

[7] viXra:1802.0123 [pdf] submitted on 2018-02-10 09:10:18

Extension of Proposition 23 from Euclid’s Elements

Authors: Prashanth R. Rao
Comments: 1 Page.

Proposition 23 states that two parallel lines in a plane never intersect. We use this definition with first and second postulate of Euclid to prove that two distinct lines through a single point cannot be parallel.
Category: Geometry

[6] viXra:1802.0092 [pdf] submitted on 2018-02-08 07:24:07

A Relationship Between a Cevian, Two Perpendicular Bisectors and a Median in an Isosceles Triangle.

Authors: Jesús Álvarez Lobo
Comments: 1 Page. Revista Escolar de la Olimpiada Iberoamericana de Matemática. Volume 18. Spanish.

A very simple solution to a geometric problem (proposed by Alex Sierra Cardenas, Medellin, Colombia) that involves a cevian, two perpendicular bisectors and a median in an isosceles triangle.
Category: Geometry

[5] viXra:1802.0091 [pdf] submitted on 2018-02-08 07:47:03

Geometry Beyond Algebra. the Theorem of Overlapped Polynomials (Top) Andits Application to the Sawa Masayoshi\'s Sangaku Problem. the Adventure Ofsolving a Mathematical Challenge Stated in 1821.

Authors: Jesús Álvarez Lobo
Comments: 47 Pages. https://arxiv.org/abs/1110.1299

This work presents for the first time a solution to the 1821 unsolved Sawa Masayoshi's problem, giving an explicit and algebraically exact solution for the symmetric case (particular case b = c, i.e., for ABC isosceles right-angled triangle), see (1.60) and (1.61). Despite the isosceles triangle restriction is not necessary, in view of the complexity of the explicit algebraic solution for the symmetric case, one can guessing the impossibility of achieving an explicit relationship for the asymmetric case (the more general case: ABC right-angled scalene triangle). For this case is given a proof of existence and uniqueness of solution and a proof of the impossibility of getting such a relationship, even implicitly, if the sextic equation (2.54) it isn't solvable. Nevertheless, in (2.56) - (2.58) it is shown the way to solve the asymmetric case under the condition that (2.54) be solvable. Furthermore, it is proved that with a slight modification in the final set of variables (F), it is still possible to establish a relation between them, see (2.59) and (2.61), which provides a bridge that connects the primitive relationship by means of numerical methods, for every given right-angled triangle ABC. And as the attempt to solve Fermat's conjecture (or Fermat's last theorem), culminated more than three centuries later by Andrew Wiles, led to the development of powerful theories of more general scope, the attempt to solve the Masayoshi's problem has led to the development of the Theory of Overlapping Polynomials (TOP), whose application to this problem reveals a great potential that might be extrapolated to other frameworks.
Category: Geometry

[4] viXra:1802.0079 [pdf] submitted on 2018-02-08 06:28:49

Wasan Geometry: 3-Isoincircles Problem. Trigonometric Analysis of a Hard Sangaku Challenge.

Authors: Jesús Álvarez Lobo
Comments: 11 Pages.

Sacred Mathematics: Japanese Temple Geometry. Fukagawa Hidetoshi - Tony Rothman. Still Harder Temple Geometry Problems: Chapter 6 - Problem 3.
Category: Geometry

[3] viXra:1802.0071 [pdf] submitted on 2018-02-07 07:09:05

La Représentation de Bonne

Authors: Abdelmajid Ben Hadj Salem
Comments: 13 Pages. In French.

This paper gives the elements of definition of the Bonne's map projection. It was used for the ancient cartography at 1/50000 scale in Tunisia and Algeria.
Category: Geometry

[2] viXra:1802.0047 [pdf] submitted on 2018-02-05 08:51:37

Calculating the Angle Between Projections of Vectors Via Geometric (Clifford) Algebra

Authors: James A. Smith
Comments: 14 Pages.

We express a problem from visual astronomy in terms of Geometric (Clifford) Algebra, then solve the problem by deriving expressions for the sine and cosine of the angle between projections of two vectors upon a plane. Geometric Algebra enables us to do so without deriving expressions for the projections themselves.
Category: Geometry

[1] viXra:1802.0036 [pdf] submitted on 2018-02-03 13:17:15

The Flow of HyperKaehler-Ricci

Authors: Antoine Balan
Comments: 2 pages, written in french

Studying the flow of Kaehler-Ricci, a flow is defined for a manifold which is HyperKaehler.
Category: Geometry