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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.
code chart ∣ web page ... inverse white circle square with upper left diagonal half black ... white square with vertical bisecting line:
Regular polygons; Description Figure Second moment of area Comment A filled regular (equiliteral) triangle with a side length of a = = [6] The result is valid for both a horizontal and a vertical axis through the centroid, and therefore is also valid for an axis with arbitrary direction that passes through the origin.
As the number of sides increases, the internal angle can come very close to 180°, and the shape of the polygon approaches that of a circle. However the polygon can never become a circle. The value of the internal angle can never become exactly equal to 180°, as the circumference would effectively become a straight line (see apeirogon). For ...
Sizes of circular features are indicated using either diametral or radial dimensions. Radial dimensions use an "R" followed by the value for the radius; Diametral dimensions use a circle with forward-leaning diagonal line through it, called the diameter symbol, followed by the value for the diameter.
For a cyclic orthodiagonal quadrilateral (one that can be inscribed in a circle), suppose the intersection of the diagonals divides one diagonal into segments of lengths p 1 and p 2 and divides the other diagonal into segments of lengths q 1 and q 2. Then [9] (the first equality is Proposition 11 in Archimedes' Book of Lemmas)
The fifth vertex is the rightmost intersection of the horizontal line with the original circle. Steps 6–8 are equivalent to the following version, shown in the animation: 6a. Construct point F as the midpoint of O and W. 7a. Construct a vertical line through F. It intersects the original circle at two of the vertices of the pentagon.
The word diagonal derives from the ancient Greek διαγώνιος diagonios, [1] "from corner to corner" (from διά- dia-, "through", "across" and γωνία gonia, "corner", related to gony "knee"); it was used by both Strabo [2] and Euclid [3] to refer to a line connecting two vertices of a rhombus or cuboid, [4] and later adopted into ...