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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.
A circle is divided into 360 degrees; subdivisions of the degree include the minute (1 ⁄ 60 of one degree) and the second (1 ⁄ 3600 of one degree). Degrees are commonly used to divide the roughly spherical shape of the Earth for geographic and cartographic purposes, e.g. when reporting latitudes and longitudes. [1] degree day
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 ...
A regular hexagonal grid This honeycomb forms a circle packing, with circles centered on each hexagon.. The honeycomb conjecture states that a regular hexagonal grid or honeycomb has the least total perimeter of any subdivision of the plane into regions of equal area.
circle division by chords Image title Illustration of the number of points ( n ), chords ( c ) and regions ( rG ) for first six terms of Moser's circle problem (OEIS A000127) by CMG Lee.
It is an icon of chemistry and is widely used in physics and other sciences. It is a depiction of the periodic law, which states that when the elements are arranged in order of their atomic numbers an approximate recurrence of their properties is evident. The table is divided into four roughly rectangular areas called blocks. Elements in the ...
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:
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 ...