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A k-map graph is a map graph derived from a set of regions in which at most k regions meet at any point. Equivalently, it is the half-square of a planar bipartite graph in which the vertex set U (the side of the bipartition not used to induce the half-square) has maximum degree k .
The Hadwiger–Nelson problem concerns the chromatic number of unit distance graphs, and more specifically of the infinite unit distance graph formed from all points of the Euclidean plane. By the de Bruijn–Erdős theorem , which assumes the axiom of choice , this is equivalent to asking for the largest chromatic number of a finite unit ...
A Voronoi diagram is a special kind of decomposition of a metric space determined by distances to a specified discrete set of objects in the space, e.g., by a discrete set of points. This diagram is named after Georgy Voronoi , also called a Voronoi tessellation , a Voronoi decomposition, or a Dirichlet tessellation after Peter Gustav Lejeune ...
In mathematics, a metric space is a set together with a notion of distance between its elements, usually called points. The distance is measured by a function called a metric or distance function. [1] Metric spaces are the most general setting for studying many of the concepts of mathematical analysis and geometry.
Mathematical puzzles are sometimes used to motivate students in teaching elementary school math problem solving techniques. [1] Creative thinking – or " thinking outside the box " – often helps to find the solution.
Goldbach’s Conjecture. One of the greatest unsolved mysteries in math is also very easy to write. Goldbach’s Conjecture is, “Every even number (greater than two) is the sum of two primes ...
The latter may occur even if the distance in the other direction between the same two vertices is defined. In the mathematical field of graph theory, the distance between two vertices in a graph is the number of edges in a shortest path (also called a graph geodesic) connecting them. This is also known as the geodesic distance or shortest-path ...
Converting ruler distance on the Mercator map into true (great circle) distance on the sphere is straightforward along the equator but nowhere else. One problem is the variation of scale with latitude, and another is that straight lines on the map (rhumb lines), other than the meridians or the equator, do not correspond to great circles.