- Titulinis
- Dalykinė ir mokslinė literatūra
- Fiziniai ir gamtos mokslai
- Matematika
- Observability and Mathematics Modeling: Hilbert, Euclid, Gauss-Bolyai-Lobachevsky, and ...
Observability and Mathematics Modeling: Hilbert, Euclid, Gauss-Bolyai-Lobachevsky, and Riemann Geometries
ISBN: 9783111679464
Autorius : Nikolai Khots
Leidimo metai: 2025
Leidėjas: De Gruyter
Puslapių skaičius: 531
Leidinio kalba: Anglų
Formatas: Kieti viršeliai
Formatas: 240×170
Autorius : Nikolai Khots
Leidimo metai: 2025
Leidėjas: De Gruyter
Puslapių skaičius: 531
Leidinio kalba: Anglų
Formatas: Kieti viršeliai
Formatas: 240×170
Aprašymas
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.
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