sahipse

Sahipse is a fictional mathematical construct used for illustrative purposes in this article. It is described as a family of plane curves defined by a distance-based constraint that depends on a nonnegative parameter s.

Definition and basic idea

Consider two fixed points F1 and F2 (foci) and two fixed lines L1 and L2. The sahipse is the locus of points P in the plane that satisfy d(P, F1) + d(P, F2) + s [d(P, L1) + d(P, L2)] = c, where d denotes distance and c is a positive constant. When s = 0, the locus reduces to a standard ellipse with foci F1 and F2. As s increases, the curve deforms smoothly, producing a continuous family of shapes known collectively as sahipse curves. The term signals the role of s in shaping the geometry, blending classic ellipse properties with line-distance terms.

Properties and behavior

In symmetric configurations where F1 and F2 lie on a common axis and L1 and L2 are parallel to that axis, sahipse curves exhibit axial symmetry about that axis. For small s, the curves resemble ellipses; for larger s, the curves become more elongated along the axis through the foci and can develop flatter regions near the ends. The family remains smooth for typical parameter ranges, and its area grows as s increases, though the exact dependence on s and the geometry of F1, F2, L1, and L2 is determined by the chosen constants.

History and context

The term sahipse appears in this article as a hypothetical example to illustrate how a parametric curve family might be described in a wiki-style entry. There are no widely cited peer-reviewed publications establishing sahipse as a real mathematical object, and the concept is presented here for pedagogical purposes and discussion of curve families.

See also

Ellipse, Limaçon, Envelope, Curve families.