Hermann Minkowski

Hermann Minkowski was a German mathematician and physicist, best known for his contributions to the field of mathematics and theoretical physics, particularly in the development of the theory of relativity. Born on June 22, 1864, and dying on January 12, 1909, Minkowski played a crucial role in the formulation of spacetime concepts.

The Abraham–Minkowski controversy refers to a longstanding debate in theoretical physics regarding the momentum of light in a medium and the way that electromagnetic waves interact with matter. Specifically, it revolves around two competing formulations for the momentum of light in a dielectric medium, attributed to physicists Max Abraham and Hermann Minkowski, both of whom derived different expressions for the momentum of photons in a medium.

The Hasse–Minkowski theorem is a result in the field of number theory, specifically concerning the theory of quadratic forms. It establishes a fundamental connection between the local and global solvability of quadratic forms over the rational numbers. In simple terms, the theorem states that a quadratic form over the rational numbers can be represented by integers if and only if it can be represented by integers when considered over the completions of the rational numbers at all finite places and at infinity (the real numbers).

The Hyperplane Separation Theorem is a fundamental result in convex geometry and functional analysis that deals with the separation of convex sets in a Euclidean space.

Minkowski's bound is a concept from number theory, particularly in the area of algebraic number fields and lattice point counting. It is named after the mathematician Hermann Minkowski. In the context of algebraic number theory, Minkowski's bound provides a way to estimate the size of the class number of a number field. More concretely, it establishes a bound on the norms of non-zero ideals in the ring of integers of a number field.

Minkowski's second theorem, which is a key result in the theory of convex bodies in the context of number theory and geometry, pertains to the volume of convex symmetric bodies in Euclidean space and their relation to lattice points. The theorem states that if \( K \) is a convex symmetric body in \( \mathbb{R}^n \) (i.e.

Minkowski's theorem is a fundamental result in the field of number theory and geometry, particularly in the context of convex geometry and the geometry of numbers. The theorem addresses the existence of certain lattice points within convex bodies in Euclidean space.

Minkowski is a crater located on the Moon's surface, specifically in the region of the Moon known as the Oceanus Procellarum (the Ocean of Storms). The crater is named after the German mathematician and physicist Hermann Minkowski, who is known for his contributions to the theory of relativity and the geometry of spacetime. Minkowski crater is characterized by its circular shape and has a relatively well-preserved structure.

The Minkowski functional, often associated with convex analysis and geometry, is a generalization of the concept of a norm. It is defined within the context of a convex set in a vector space, particularly in relation to a symmetric convex body.

The Minkowski problem is a classical problem in the field of convex geometry, specifically concerning the characterization of convex bodies (or polytopes) based on their surface area measures. The problem is named after the mathematician Hermann Minkowski.

The Minkowski sausage is a geometric construct used in the field of topology and geometric measure theory, particularly in the study of the properties of sets in Euclidean space. Specifically, it refers to a way of "thickening" a curve in Euclidean space to create a three-dimensional shape. Given a continuous curve \( C \) in three-dimensional space, the Minkowski sausage is formed by taking a tubular neighborhood around the curve.

The Minkowski–Bouligand dimension, also known as the box-counting dimension, is a concept in fractal geometry that provides a way to measure the dimensionality of a set in a more general sense than traditional Euclidean dimensions. It is particularly useful for non-integer dimensions, which often arise in fractals and irregular geometric shapes.

The Minkowski–Hlawka theorem is a result in number theory and the geometry of numbers that pertains to the representation of integer points in geometric space. Specifically, it addresses the existence of points with integer coordinates within certain convex bodies in Euclidean space.

The Smith–Minkowski–Siegel mass formula is a result in the theory of quadratic forms and arithmetic geometry. It provides a way to compute the mass of an orbit of a quadratic form under the action of a group, typically the group of diagonalizable matrices over certain rings. This formula is particularly relevant in the study of quadratic forms over global fields and local fields.