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The converse may or may not be true, and even if true, the proof may be difficult. For example, the four-vertex theorem was proved in 1912, but its converse was proved only in 1997. [3] In practice, when determining the converse of a mathematical theorem, aspects of the antecedent may be taken as establishing context.
In the monoid of binary endorelations on a set (with the binary operation on relations being the composition of relations), the converse relation does not satisfy the definition of an inverse from group theory, that is, if is an arbitrary relation on , then does not equal the identity relation on in general.
The intercept theorem, also known as Thales's theorem, basic proportionality theorem or side splitter theorem, is an important theorem in elementary geometry about the ratios of various line segments that are created if two rays with a common starting point are intercepted by a pair of parallels.
Pages in category "Physics theorems" ... Parallel axis theorem; Pauthenier equation; Perpendicular axis theorem; Plastic limit theorems; Pokhozhaev's identity;
The converse of the theorem is true and is called Israel's theorem. [1] [2] The converse is not true in Newtonian gravity. [3] [4] The theorem was proven in 1923 by George David Birkhoff (author of another famous Birkhoff theorem, the pointwise ergodic theorem which lies at the foundation of ergodic theory).
Laws of physics are translationally invariant under a spatial translation if they do not distinguish different points in space. According to Noether's theorem , space translational symmetry of a physical system is equivalent to the momentum conservation law .
Time-translation symmetry is the law that the laws of physics are unchanged (i.e. invariant) under such a transformation. Time-translation symmetry is a rigorous way to formulate the idea that the laws of physics are the same throughout history. Time-translation symmetry is closely connected, via Noether's theorem, to conservation of energy. [1]
In physics and mathematics, and especially differential geometry and gauge theory, the Yang–Mills equations are a system of partial differential equations for a connection on a vector bundle or principal bundle. They arise in physics as the Euler–Lagrange equations of the Yang–Mills action functional. They have also found significant use ...