is an equireciprocal point if, for every chord ![[x,y]](/images/equations/EquireciprocalPoint/Inline2.svg)
of a curve 
, 
satisfies
 |
for some constant 
.
The foci of an ellipse are
equichordal points.
Equireciprocal Point
See also
Equichordal Point, Equiproduct PointExplore with Wolfram|Alpha
References
Croft, H. T.; Falconer, K. J.; and Guy, R. K. Unsolved Problems in Geometry. New York: Springer-Verlag, p. 10, 1991.Falconer, K. J. "On the Equireciprocal Point Problem." Geom. Dedicata 14, 113-126, 1983.Hallstrom, A. P. "Equichordal and Equireciprocal Points." Bogasici Univ. J. Sci. 2, 83-88, 1974.Klee, V. "Can a Plane Convex Body have Two Equireciprocal Points?" Amer. Math. Monthly 76, 54-55, 1969.Klee, V. "Correction to 'Can a Plane Convex Body have Two Equireciprocal Points?' " Amer. Math. Monthly 78, 114, 1971.Referenced on Wolfram|Alpha
Equireciprocal PointCite this as:
Weisstein, Eric W. "Equireciprocal Point." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/EquireciprocalPoint.html