Abstract
Elliptic curves (nonsingular plane cubic curves) have a natural group structure. The so-called chord and. tangent addition rule is based on the fact that, in general, a straight line intersects a cubic curve in three points. This group structure is one of the main tools in the study of arithmnetic properties of elliptic curves ([6], [9]). Elliptic curves play a central role in the proof of Fermat's last theorem by A. Wiles [14] and they enter even in areas like ciyptography, with Lenstra's elliptic curve algorithm [7]. The purpose of this article is to apply this simple group structure to study geometric properties of a particular class of cubic curves, arising in the following problem of Euclidean metric geometiy (see FIGURE 1):
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