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Projective range

In mathematics, a projective range is a set of points in projective geometry considered in a unified fashion. A projective range may be a projective line or a conic. A projective range is the dual of a pencil of lines on a given point. For instance, a correlation interchanges the points of a projective range with the lines of a pencil. A projectivity is said to act from one range to another, though the two ranges may coincide as sets.

Conic ranges
When a conic is chosen for a projective range, and a particular point E on the conic is selected as origin, then addition of points may be defined as follows: : Let A and B be in the range (conic) and AB the line connecting them. Let L be the line through E and parallel to AB. The "sum of points A and B", A + B, is the intersection of L with the range. The circle and hyperbola are instances of a conic and the summation of angles on either can be generated by the method of "sum of points", provided points are associated with angles on the circle and hyperbolic angles on the hyperbola. ==References==
Source: Wikipedia ↗
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