scholarly journals Absolute Geometry: From Basics to the π-rule of the Ф-invariant Physics

2021 ◽  
Vol 4 (4) ◽  
Keyword(s):  
Absolute Geometry

This is to clarify in more detail some basic aspects of absolute geometry and discuss what is the π-rule in physics unified by the universal Ф-invariance

Bireflectionality in Absolute Geometry

1989 ◽  
Vol 32 (1) ◽  
pp. 54-63 ◽  
Author(s):  
Dragoslav Ljubić
Keyword(s):  
General Result ◽  
3 Dimensional ◽  
Absolute Geometry

AbstractIf G is any group then g ∊ G is called an involution if g ≠ 1 and g o g = 1. A group G is called bireflectional if every element in G is a product of two involutions. It is known that 2- dimensional, 3- dimensional, and some types of n-dimensional (n > 3) absolute geometries (in the sense of H. Kinder) are bireflectional. In this article the author proves the general result that every n-dimensional absolute geometry is bireflectional.

Existence of special rainbow triangles in weak geometries

2019 ◽  
Vol 26 (4) ◽  
pp. 489-498
Author(s):  
Victor Pambuccian
Keyword(s):  
Orthogonality Relation ◽  
Absolute Geometry ◽  
Acute Triangle ◽  
Definition Of ◽  
Meaningful Definition

Abstract We show that, in any ordered plane with a symmetric orthogonality relation which allows for a meaningful definition of acute and obtuse angles, in which all points are colored with three colors, such that each color is used at least once, there must exist both an acute triangle whose vertices have all three colors and an obtuse triangle with the same property. We also show that, in both a geometry endowed with an orthogonality relation, in which there is a reflection in every line, in which all right angles are bisectable, which satisfies Bachmann’s Lotschnittaxiom (the perpendiculars raised on the sides of a right angle intersect), and in plane absolute geometry, in which all points are colored with three colors, such that each color is used at least once, there exists a right triangle with all vertices of different colors.

Legendre-like Theorems in a General Absolute Geometry

2007 ◽  
Vol 51 (1-2) ◽  
pp. 61-71 ◽  
Author(s):  
Helmut Karzel ◽  
Mario Marchi ◽  
Silvia Pianta
Keyword(s):  
Absolute Geometry

Axioms for Absolute Geometry

1968 ◽  
Vol 20 ◽  
pp. 158-181 ◽  
Author(s):  
J. F. Rigby
Keyword(s):  
Hyperbolic Geometry ◽  
Euclidean Geometry ◽  
Absolute Geometry

The axioms of Euclidean geometry may be divided into four groups: the axioms of order, the axioms of congruence, the axiom of continuity, and the Euclidean axiom of parallelism (6). If we omit this last axiom, the remaining axioms give either Euclidean or hyperbolic geometry. Many important theorems can be proved if we assume only the axioms of order and congruence, and the name absolute geometry is given to geometry in which we assume only these axioms. In this paper we investigate what can be proved using congruence axioms that are weaker than those used previously.

Islamic star patterns in absolute geometry

2004 ◽  
Vol 23 (2) ◽  
pp. 97-119 ◽  
Author(s):  
Craig S. Kaplan ◽  
David H. Salesin
Keyword(s):  
Absolute Geometry

Segment Trisection in Absolute Geometry

1978 ◽  
Vol 51 (2) ◽  
pp. 124 ◽  
Author(s):  
Hubert J. Ludwig
Keyword(s):  
Absolute Geometry

The Centroid in Absolute Geometry

1960 ◽  
Vol 67 (9) ◽  
pp. 885
Author(s):  
Curtis M. Fulton
Keyword(s):  
Absolute Geometry
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