We show here that is the smallest such solution (its Euclidean norm is uniquely minimum).
Euclidean space | Euclidean vector | Euclidean geometry | non-Euclidean geometry | Euclidean group | Euclidean distance | Euclidean | Euclidean algorithm |
Distance measures can be classified into Euclidean measures and non-Euclidean measures depending on whether the triangle inequality holds.
This honeycomb is last in the series of Thorold Gosset in 1900, listing polytopes and honeycombs constructed entirely of regular facets, although his list ended with the 8-dimensional the Euclidean honeycomb, 521.
The Euclidean shortest path problem is a problem in computational geometry: given a set of polyhedral obstacles in a Euclidean space, and two points, find the shortest path between the points that does not intersect any of the obstacles.
A flat torus can be isometrically embedded in three-dimensional Euclidean space with a C1 map (by the Nash embedding theorem) but not with a C2 map, and the Clifford torus provides an isometric analytic embedding of a flat torus in four dimensions.
Martin Gardner, Non-Euclidean Geometry, Chapter 14 of The Colossal Book of Mathematics, W. W.Norton & Company, 2001, ISBN 0-393-02023-1
Hadwiger–Nelson problem on the chromatic number of unit distance graphs in the Euclidean plane
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Hadwiger's theorem characterizing measure functions in Euclidean spaces
He completed his PhD at Caltech in mathematics and physics in 1925 under Harry Bateman, with the dissertation, “On Dynamical Space-Times Which Contain a Conformal Euclidean 3-Space”.
He received his Ph.D. in 1927 from Johns Hopkins University, under the supervision of Frank Morley; his dissertation was titled Lagrange Resolvents in Euclidean Geometry.
Minkowski–Bouligand dimension (also called the metric dimension), a way of determining the dimension of a fractal set in a Euclidean space by counting the number of fixed-size boxes needed to cover the set as a function of the box size
Shing-Tung Yau received the Fields Medal at the International Congress of Mathematicians in Warsaw in 1982 for his work in global differential geometry and elliptic partial differential equations, particularly for solving such difficult problems as the Calabi conjecture of 1954, and a problem of Hermann Minkowski in Euclidean spaces concerning the Dirichlet problem for the real Monge–Ampère equation.
Bernard H. Lavenda, (2012) " A New Perspective on Relativity : An Odyssey In Non-Euclidean Geometries", World Scientific, pp.
Euclidean geometry, where Euclidean space is viewed as the natural representation space of the group of Euclidean motions
Since Ricci curvature measures the amount by which the volume of a small geodesic ball deviates from the volume of a ball in Euclidean space, small geodesic balls will have no volume deviation, but their "shape" may vary from the shape of the standard ball in Euclidean space.
Hyperplane separation theorem (geometry) is either of two theorems about disjoint convex sets in n-dimensional Euclidean space.
Edwin Bidwell Wilson & Gilbert N. Lewis (1912) "The space-time manifold of relativity. The non-Euclidean geometry of mechanics and electromagnetics", Proceedings of the American Academy of Arts and Sciences 48:387–507.
Its five chapters concern Euclidean and non-Euclidean geometry, and literalist and non-literalist views on the meaning of numbers.
He also contributed to Obscura's highly acclaimed album Omnivium, playing a guitar solo on the song "Euclidean Elements".
Therefore, the Euclidean shortest path problem may be decomposed into two simpler subproblems: constructing the visibility graph, and applying a shortest path algorithm such as Dijkstra's algorithm to the graph.