- Axiom(as something that may be necessary or redundant in a logical system)
- A basic assumption or rule that you accept as true without proof, which then serves as the foundation for building other conclusions.
- Finsler norms(as alternative geometries that might fit physical space)
- A mathematical way of measuring distances in space that is more flexible and general than the familiar straight-line distance formula.
- Free mobility(as a geometric principle)
- The idea that you can move an object around in space without changing its shape or size, and the physical laws stay the same no matter where you move it.
- Non-quadratic(as unusual types of geometry that might describe space)
- Not using squared terms; describes alternative ways of measuring distance that don't follow the standard Pythagorean formula.
- Physical geometry(as the geometry that describes reality)
- The actual shape and structure of real space and time in the universe, as opposed to pure abstract mathematics.
- Quadratic(as an example of a different type of threshold)
- A mathematical relationship that involves squaring numbers, creating a curved pattern rather than a straight line.
- Weyl's Postulate(Relativistic cosmology)
- The postulate that the worldlines of fundamental particles (galaxies) in the cosmological fluid are non-intersecting geodesics, yielding a unique geodesic and unique matter velocity at each spacetime point, and defining a privileged class of observers
- Élie Cartan(as a historical figure in mathematics and geometry)
- A French mathematician (1869–1951) who developed new ways of understanding geometry and shapes using tools called differential forms, which became foundational for modern physics.