spaces can be embedded in the Hilbert cube; that is, can be viewed as subspaces of the Hilbert cube (see below). The Hilbert cube is best defined as the topological...

David Hilbert Foundations of geometry Hilbert C*-module Hilbert cube Hilbert curve Hilbert matrix Hilbert metric Hilbert–Mumford criterion Hilbert number...

In geometry, a cube or regular hexahedron is a three-dimensional solid object bounded by six congruent square faces, a type of polyhedron. It has twelve...

The third of Hilbert's list of mathematical problems, presented in 1900, was the first to be solved. The problem is related to the following question:...

cubes problem, discusses whether every integer is the sum of four cubes of integers Hilbert, David (1909). "Beweis für die Darstellbarkeit der ganzen Zahlen...

mathematics, the Menger sponge (also known as the Menger cube, Menger universal curve, Sierpinski cube, or Sierpinski sponge) is a fractal curve. It is a three-dimensional...

island H-fractal Hénon map Hexaflake Hilbert curve Ikeda map attractor Iterated function system Jerusalem cube Julia set Koch curve Koch snowflake L-system...

whenever it shows a smaller inner cube inside a larger outer cube. The eight lines connecting the vertices of the two cubes in this case represent a single...

theorem implies that every Hilbert cube manifold as well as the (rather different, for example not locally compact) Hilbert manifolds and Banach manifolds...

dissections can tile space. It is named after Max Dehn, who used it to solve Hilbert's third problem by proving that certain polyhedra with equal volume cannot...

side of a cube whose volume is twice the volume of a cube with a given side.: p. 29  Hippocrates and Menaechmus showed that the volume of the cube could be...

dimension as a theoretical construct. These theories make reference to Hilbert space, a concept that postulates an infinite number of mathematical dimensions...

insufficient as a basis of Euclidean geometry, so other systems (such as Hilbert's axioms without the parallel axiom) are used instead. In Euclid's Elements...

include sums of non-negative cubes and sums of rational cubes. All integers have a representation as a sum of rational cubes, but it is unknown whether...

compact, contractible, path connected and locally path connected. The Hilbert cube is obtained by taking a topological product of countably many copies...

on our intuition of space. Such axioms, now known as Hilbert's axioms, were given by David Hilbert in 1894 in his dissertation Grundlagen der Geometrie...

the cube. The cube can be dissected into six such 3-orthoschemes four different ways, with all six surrounding the same √3 cube diagonal. The cube can...

Cantor space, Cantor cube Space-filling curve Topologist's sine curve Uniform norm Weak topology Strong topology Hilbert cube Lower limit topology Sorgenfrey...

points, not all on the same plane, the convex hull is a convex polyhedron. Cubes and pyramids are examples of convex polyhedra. A polyhedron is a generalization...

whether the applicable geometry was Euclidean or non-Euclidean. Hilbert's axioms: Hilbert's axioms had the goal of identifying a simple and complete set...

logic Hilbert space – Type of topological vector space Hilbert's Nullstellensatz – Relation between algebraic varieties and polynomial ideals Hilbert's syzygy...

Sanskrit verses, was divided into two sections: "basic operations" (including cube roots, fractions, ratio and proportion, and barter) and "practical mathematics"...

diagonals of a cube, and the points as the eight vertices of the cube, its center, and the three points where groups of four parallel cube edges meet the...

of spaces, such as Euclidean spaces, linear spaces, topological spaces, Hilbert spaces, or probability spaces, it does not define the notion of "space"...

In 1637, Pierre de Fermat scribbled on the margin of his copy of Arithmetica: "It is impossible to separate a cube into two cubes, or a fourth power...

York 1968 (Chelsea) http://www.emis.de/classics/Riemann/. Also in Ewald, William B., ed., 1996 "From Kant to Hilbert: A Source Book in the Foundations of...

dimensions Space group Symmetry group Translational symmetry Wallpaper group Hilbert's axioms Locus Line Line segment Parallel Angle Concurrent lines Adjacent...

geometry) Hilbert–Schmidt theorem (functional analysis) Hilbert–Speiser theorem (cyclotomic fields) Hilbert–Waring theorem (number theory) Hilbert's irreducibility...

the University of Munich, to be a special assistant for physics to David Hilbert at the University of Göttingen, to replace Paul Peter Ewald, whom Sommerfeld...

extended to an ideal of the Hilbert class field. This means that there is an element of the ring of integers of the Hilbert class field, which is an ideal...