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Exploring the shape of the universe, this monograph addresses how to measure distances in physical space, questioning whether to follow straight lines or curved paths. It presents a mathematical proof that space is Euclidean for distances around 10 AU, confirming assumptions held by physicists. The work extends classical Newtonian gravitation into non-Euclidean spaces using the cotangent potential, originally proposed by Ernest Schering. This research uncovers intriguing connections among classical dynamics, non-Euclidean geometry, geometric topology, Lie groups, and polytopes.
Nákup knihy
Relative Equilibria of the Curved N-Body Problem, Florin Diacu
- Jazyk
- Rok vydania
- 2012
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- Titul
- Relative Equilibria of the Curved N-Body Problem
- Jazyk
- anglicky
- Autori
- Florin Diacu
- Vydavateľ
- Atlantis Press
- Rok vydania
- 2012
- Väzba
- pevná
- Počet strán
- 160
- ISBN13
- 9789491216671
- Kategórie
- Matematika
- Anotácia
- Exploring the shape of the universe, this monograph addresses how to measure distances in physical space, questioning whether to follow straight lines or curved paths. It presents a mathematical proof that space is Euclidean for distances around 10 AU, confirming assumptions held by physicists. The work extends classical Newtonian gravitation into non-Euclidean spaces using the cotangent potential, originally proposed by Ernest Schering. This research uncovers intriguing connections among classical dynamics, non-Euclidean geometry, geometric topology, Lie groups, and polytopes.