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The number of points (n), chords (c) and regions (r G) for first 6 terms of Moser's circle problem. In geometry, the problem of dividing a circle into areas by means of an inscribed polygon with n sides in such a way as to maximise the number of areas created by the edges and diagonals, sometimes called Moser's circle problem (named after Leo Moser), has a solution by an inductive method.
Dividing a circle into areas – Problem in geometry; Equal incircles theorem – On rays from a point to a line, with equal inscribed circles between adjacent rays; Five circles theorem – Derives a pentagram from five chained circles centered on a common sixth circle; Gauss circle problem – How many integer lattice points there are in a circle
The fifth column (k = 4) gives the maximum number of regions in the problem of dividing a circle into areas for n + 1 points, where n ≥ 4. [6] In general, the (k + 1)th column gives the maximum number of regions in k-dimensional space formed by n − 1 (k − 1)-dimensional hyperplanes, for n ≥ k. [7]
Chord: a line segment whose endpoints lie on the circle, thus dividing a circle into two segments. Circumference: the length of one circuit along the circle, or the distance around the circle. Diameter: a line segment whose endpoints lie on the circle and that passes through the centre; or the length of such a line segment. This is the largest ...
Explicitly, we imagine dividing up a circle into triangles, each with a height equal to the circle's radius and a base that is infinitesimally small. The area of each of these triangles is equal to /. By summing up (integrating) all of the areas of these triangles, we arrive at the formula for the circle's area:
This glossary of chemistry terms is a list of terms and definitions relevant to chemistry, including chemical laws, diagrams and formulae, laboratory tools, glassware, and equipment. Chemistry is a physical science concerned with the composition, structure, and properties of matter , as well as the changes it undergoes during chemical reactions ...
The region of the plane between two concentric circles is an annulus, and analogously the region of space between two concentric spheres is a spherical shell. [6] For a given point c in the plane, the set of all circles having c as their center forms a pencil of circles. Each two circles in the pencil are concentric, and have different radii.
Let be a metric space with distance function .Let be a set of indices and let () be a tuple (indexed collection) of nonempty subsets (the sites) in the space .The Voronoi cell, or Voronoi region, , associated with the site is the set of all points in whose distance to is not greater than their distance to the other sites , where is any index different from .
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