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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.
In statistics, the Lehmann–Scheffé theorem is a prominent statement, tying together the ideas of completeness, sufficiency, uniqueness, and best unbiased estimation. [1] The theorem states that any estimator that is unbiased for a given unknown quantity and that depends on the data only through a complete , sufficient statistic is the unique ...
Big O notation is a mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity. Big O is a member of a family of notations invented by German mathematicians Paul Bachmann, [1] Edmund Landau, [2] and others, collectively called Bachmann–Landau notation or asymptotic notation.
The theorem was first proven by Emanuel Lasker for the special case of polynomial rings and convergent power series rings, and was proven in its full generality by Emmy Noether . The Lasker–Noether theorem is an extension of the fundamental theorem of arithmetic , and more generally the fundamental theorem of finitely generated abelian groups ...
The proof of Synge's theorem can be summarized as follows. [1] Given a geodesic S 1 → M with an orthogonal and parallel vector field along the geodesic (i.e. a parallel section of the normal bundle to the geodesic), then Synge's earlier computation of the second variation formula for arclength shows immediately that the geodesic may be ...
Theorem: In the euclidean space a function () is an L 1 multiplier (equivalently an L ∞ multiplier) if and only if there exists a finite Borel measure μ such that m is the Fourier transform of μ. (The "if" part is a simple calculation.
John Nash used the theorem in game theory to prove the existence of an equilibrium strategy profile. The theorem proved its worth in more than one way. During the 20th century numerous fixed-point theorems were developed, and even a branch of mathematics called fixed-point theory. [38] Brouwer's theorem is probably the most important. [39]
In physics, the special theory of relativity, or special relativity for short, is a scientific theory of the relationship between space and time.In Albert Einstein's 1905 paper, On the Electrodynamics of Moving Bodies, the theory is presented as being based on just two postulates: [p 1] [1] [2]