Hermann Minkowski in the context of "Surface area"

The Minkowski content (named after Hermann Minkowski), or the boundary measure, of a set is a basic concept that uses concepts from geometry and measure theory to generalize the notions of length of a smooth curve in the plane, and area of a smooth surface in space, to arbitrary measurable sets.

It is typically applied to fractal boundaries of domains in the Euclidean space, but it can also be used in the context of general metric measure spaces.

In physics, Minkowski space (or Minkowski spacetime) (/mɪŋˈkɔːfski, -ˈkɒf-/) is the main mathematical description of spacetime in the absence of gravitation. It combines inertial space and time manifolds into a four-dimensional model.

The model helps show how a spacetime interval between any two events is independent of the inertial frame of reference in which they are recorded. Mathematician Hermann Minkowski developed it from the work of Hendrik Lorentz, Henri Poincaré, and others, and said it "was grown on experimental physical grounds".

Taxicab geometry or Manhattan geometry is geometry where the familiar Euclidean distance is ignored, and the distance between two points is instead defined to be the sum of the absolute differences of their respective Cartesian coordinates, a distance function (or metric) called the taxicab distance, Manhattan distance, or city block distance. The name refers to the island of Manhattan, or generically any planned city with a rectangular grid of streets, in which a taxicab can only travel along grid directions. In taxicab geometry, the distance between any two points equals the length of their shortest grid path. This different definition of distance also leads to a different definition of the length of a curve, for which a line segment between any two points has the same length as a grid path between those points rather than its Euclidean length.

The taxicab distance is also sometimes known as rectilinear distance or L distance (see L space). This geometry has been used in regression analysis since the 18th century, and is often referred to as LASSO. Its geometric interpretation dates to non-Euclidean geometry of the 19th century and is due to Hermann Minkowski.

Hermann Klaus Hugo Weyl (/vaɪl/; German: [vaɪl]; 9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist, logician and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, he is associated with the University of Göttingen tradition of mathematics, represented by Carl Friedrich Gauss, David Hilbert and Hermann Minkowski.

His research has had major significance for theoretical physics as well as purely mathematical disciplines such as number theory. He was one of the most influential mathematicians of the twentieth century, and an important member of the Institute for Advanced Study during its early years.

Max Born (German: [ˈmaks ˈbɔʁn] ; 11 December 1882 – 5 January 1970) was a German–British theoretical physicist who was instrumental in the development of quantum mechanics. He also made contributions to solid-state physics and optics, and supervised the work of a number of notable physicists in the 1920s and 1930s. He shared the 1954 Nobel Prize in Physics with Walther Bothe "for his fundamental research in quantum mechanics, especially in the statistical interpretation of the wave function."

Born entered the University of Göttingen in 1904, where he met the three renowned mathematicians Felix Klein, David Hilbert, and Hermann Minkowski. He wrote his Ph.D. thesis on the subject of the stability of elastic wires and tapes, winning the university's Philosophy Faculty Prize. In 1905, he began researching special relativity with Minkowski, and subsequently wrote his habilitation thesis on the Thomson model of the atom. A chance meeting with Fritz Haber in Berlin in 1918 led to discussion of how an ionic compound is formed when a metal reacts with a halogen, which is now known as the Born–Haber cycle.

In fractal geometry, the Minkowski–Bouligand dimension, also known as Minkowski dimension or box-counting dimension, is a way of determining the fractal dimension of a bounded set ${\textstyle S}$ in a Euclidean space ${\textstyle \mathbb {R} ^{n}}$, or more generally in a metric space ${\textstyle (X,d)}$. It is named after the Polish mathematician Hermann Minkowski and the French mathematician Georges Bouligand.

To calculate this dimension for a fractal ${\textstyle S}$, imagine this fractal lying on an evenly spaced grid and count how many boxes are required to cover the set. The box-counting dimension is calculated by seeing how this number changes as we make the grid finer by applying a box-counting algorithm.

Geometry of numbers, also known as geometric number theory, is the part of number theory which uses geometry for the study of algebraic numbers. Typically, a ring of algebraic integers is viewed as a lattice in ${\displaystyle \mathbb {R} ^{n},}$ and the study of these lattices provides fundamental information on algebraic numbers. Hermann Minkowski (1896) initiated this line of research at the age of 26 in his work The Geometry of Numbers.

The geometry of numbers has a close relationship with other fields of mathematics, especially functional analysis and Diophantine approximation, the problem of finding rational numbers that approximate an irrational quantity.