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

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

The Holy Trinity of Geometry: Beauty, Virtue & Truth

The virtue of absolute geometry is its accessibility to the ordinary human mind coupled with certain degree of intuition which is kind of connectedness of the human brain to the universal logico-mathematical machinery. In the end all the problem of existence reduces to the elementary operations within the continuum of natural numbers. Nontriviality and consistence of the system make the beauty of geometry. Geometry’s last truths prove to be written in beautiful and mnemonical aphorisms

Fundamental Theorems of Pure Mathematics & Absolute Geometry

The superunified field theory consists of a row of discoveries in the realm of pure mathematics. It is two centuries ago that Karl Gauss unified higher arithmetic (number theory), algebra and geometry into what is called pure mathematics. The latter, however, still remains without its fundamental theorem despite that arithmetic and algebra, or even analysis, have their own.

Quantum Gravitation Solutions

This is intended to clarify the so called problem of quantum gravitation. In absolute geometry space-time is intrinsically quantum-gravitational implying that there is no need to try to quantize gravity.

Superunified Field Theory

This is a briefest possible introduction to the absolute geometry of space, time and matter. Absolute geometry or the post-Euclidean geometry does automatically lead to the superunified theory of quantized fields and fundamental interactions. In general, we have eventually constructed the ultimate system of universal mathematical harmony observed by us as the physical Universe. No work in theoretical physics and pure mathematics directly precedes to this theory we propose. Instead, it accomplishes original Pythagorean (arithmetisation) znd Platonic (geometrization) concepts of natural philosophy integrated afterwards by Jiordano Bruno.

Existence of special rainbow triangles in weak geometries

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.