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Thomsen's theorem, named after Gerhard Thomsen, is a theorem in elementary geometry. It shows that a certain path constructed by line segments being parallel to the edges of a triangle always ends up at its starting point.
Thomson's problem is related to the 7th of the eighteen unsolved mathematics problems proposed by the mathematician Steve Smale — "Distribution of points on the 2-sphere". [2] The main difference is that in Smale's problem the function to minimise is not the electrostatic potential 1 r i j {\displaystyle 1 \over r_{ij}} but a logarithmic ...
Hasse–Arf theorem (local class field theory) Hilbert's theorem 90 (number theory) Isomorphism extension theorem (abstract algebra) Joubert's theorem ; Lagrange's theorem (number theory) Mason–Stothers theorem (polynomials) Polynomial remainder theorem (polynomials) Primitive element theorem (field theory) Rational root theorem (algebra ...
Let = + and ¯ = where and are real.. Let () = (,) + (,) be any holomorphic function.. Example 1: = (+) + Example 2: = + In his article, [1] Milne ...
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Diagram of the fundamental theorem on homomorphisms. Let G and H be groups, and let f : G → H be a homomorphism.Then: The kernel of f is a normal subgroup of G,; The image of f is a subgroup of H, and
Pythagorean theorem: It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. The theorem can be written as an equation relating the lengths of the sides a, b and the hypotenuse c, sometimes called the Pythagorean equation: [6]
Phase portrait showing saddle-node bifurcation. Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family of curves, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations.