Curved_geometries | TriviaQuestions.online

⭐ In the context of Axioms, Curved_geometries rely on which characteristic of these foundational statements to establish their unique properties?

Curved geometries, like Euclidean geometry, are built upon a set of axioms – statements accepted as true to begin the deductive reasoning process, rather than being proven through observation or experimentation.

⭐ Core Definition: Curved geometries

Curved space often refers to a spatial geometry which is not "flat", where a flat space has zero curvature, as described by Euclidean geometry. Curved spaces can generally be described by Riemannian geometry, though some simple cases can be described in other ways.

Curved spaces play an essential role in general relativity, where gravity is often visualized as curved spacetime. The Friedmann–Lemaître–Robertson–Walker metric is a curved metric which forms the current foundation for the description of the expansion of the universe and the shape of the universe. The fact that photons have no mass yet are distorted by gravity, means that the explanation would have to be something besides photonic mass. Hence, the belief that large bodies curve space and so light, traveling on the curved space will, appear as being subject to gravity. It is not, but it is subject to the curvature of space.

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Curved geometries in the context of Axiom

An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word ἀξίωμα (axíōma), meaning 'that which is thought worthy or fit' or 'that which commends itself as evident'.

The precise definition varies across fields of study. In classic philosophy, an axiom is a statement that is so evident or well-established, that it is accepted without controversy or question. In modern logic, an axiom is a premise or starting point for reasoning.

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