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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 cyclic polygon has each of its vertices on a particular circle, called the circumcircle or circumscribed circle. The centre of the circumcircle, called the circumcentre, can be considered a centre of the polygon. If a polygon is both tangential and cyclic, it is called bicentric. (All triangles are bicentric, for example.) The incentre and ...
The challenge is to divide the circle into four equal arcs using only a compass. [1] [2] Napoleon was known to be an amateur mathematician, but it is not known if he either created or solved the problem. Napoleon's friend the Italian mathematician Lorenzo Mascheroni introduced the limitation of using only a compass (no straight edge) into ...
A circle bounds a region of the plane called a disc. The circle has been known since before the beginning of recorded history. Natural circles are common, such as the full moon or a slice of round fruit. The circle is the basis for the wheel, which, with related inventions such as gears, makes much of modern
Maximise area of smallest region by using 3-fold symmetry with the 2 inscribed triangles offset by 48.71°. 23:27, 8 April 2019: ... Dividing a circle into areas;
In mathematics and physics, the centroid, also known as geometric center or center of figure, of a plane figure or solid figure is the arithmetic mean position of all the points in the surface of the figure. [further explanation needed] The same definition extends to any object in -dimensional Euclidean space. [1]
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The power diagram of a set of circles divides the plane into regions within which the circle minimizing the power is constant. More generally, French mathematician Edmond Laguerre defined the power of a point with respect to any algebraic curve in a similar way.