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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.
An n-pointed magic star is a star polygon with Schläfli symbol {n/2} [1] in which numbers are placed at each of the n vertices and n intersections, such that the four numbers on each line sum to the same magic constant. [2] A normal magic star contains the integers from 1 to 2n with no numbers repeated. [3]
In his work titled Essays upon the Mathematics of Mordente: One Hundred and Sixty Articles against the Mathematicians and Philosophers of this Age (Prague: 1588), [2] Italian philosopher, cosmological theorist, and Hermetic occultist Giordano Bruno used the unicursal hexagram symbol to represent Figura Amoris ("figure of love") [2] part of the Hermetic trinity in his mathesis.
A six-pointed star, like a regular hexagon, can be created using a compass and a straight edge: . Make a circle of any size with the compass. Without changing the radius of the compass, set its pivot on the circle's circumference, and find one of the two points where a new circle would intersect the first circle.
The circle is an instance of a conic section and the nine-point circle is an instance of the general nine-point conic that has been constructed with relation to a triangle ABC and a fourth point P, where the particular nine-point circle instance arises when P is the orthocenter of ABC.
At this point, most kids would have elaborated their calculations showing that each dime is worth $0.10, therefore making Bobby the owner of $0.40 while Amy's pennies amount to $0.30.
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A magic circle can be derived from one or more magic squares by putting a number at each intersection of a circle and a spoke. Additional spokes can be added by replicating the columns of the magic square. In the example in the figure, the following 4 × 4 most-perfect magic square was copied into the upper part of the magic circle. Each number ...