Observability and Mathematics Modeling

Hilbert, Euclid, Gauss-Bolyai-Lobachevsky, and Riemann Geometries
1. Auflage 2025
ISBN: 978-3-11-167946-4
Verlag: De Gruyter

Buch, Englisch, 428 Seiten, Format (B × H): 170 mm x 240 mm, Gewicht: 846 g

Observability in Mathematics were developed by authors based on denial of infinity idea. We introduce Observers into arithmetic, and arithmetic becomes dependent on Observers. And after that the basic mathematical parts also become dependent on Observers. One of such parts is geometry. Geometry plays important role not only in pure Mathematics but in contemporary Physics, for example, in Relativity theory, Quantum Yang-Mills theory. We call New Geometry both Observers in arithmetics and in geometry. We reconsider the basis of classic geometry (points, straight lines, planes and space) from this Mathematics point of view. The relations of connection, order, parallels (Euclid, Gauss-Bolyai-Lobachevsky, Riemann), congruence, continuity are discovered and have new properties. We show that almost all classic geometry theorems are satisfied in Mathematics with Observers geometry with probabilities less than 1.

That means classic geometries are not a limiting cases of the Observer’s geometry, but are only particular cases. And new geometry opens the road to reconsider differential geometry, algebraic geometry, geometric algebra, topology, and also to reconsider geometrical applications to various parts of contemporary physics.

We proved that Mathematics with Observers gives a birth a new geometry.

Zielgruppe

Researchers, graduate students in Geometry, Mathematical Physics,

Autoren/Hrsg.

Khots, Nikolai

Khots, Boris

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Naturwissenschaften Astronomie Astronomie: Allgemeines
• Mathematik | Informatik Mathematik Geometrie
• Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz

Über Autor(innen)

Nikolai Khots, Senior in High School, Eagle Scout, Top ten percent ranked in class, 4.5 GPA, 5 club positions, member of the American Mathematical Society since 2022, one math book published (with co-author Boris Khots).

Boris Khots, Self-Employment, Independent researcher, member of the American Mathematical Society since 1995. More than 150 scientific publications. Main research focus - mathematics (mathematics with observers, Lie groups and algebras) and it’s application to physics.