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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.
Another argument for the impossibility of circular realizations, by Helge Tverberg, uses inversive geometry to transform any three circles so that one of them becomes a line, making it easier to argue that the other two circles do not link with it to form the Borromean rings. [27] However, the Borromean rings can be realized using ellipses. [2]
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.
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A math circle is an extracurricular activity intended to enrich students' understanding of mathematics. The concept of math circle came into being in the erstwhile USSR and Bulgaria , around 1907, with the very successful mission to "discover future mathematicians and scientists and to train them from the earliest possible age".
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