6 papers · 1 filter
On the concept of center for geometric objects and related problems
M. Magdalena Martínez-Rico, L. Felipe Prieto-Martínez, R. Sánchez-Cauce
In this work, we review the concept of center of a geometric object as an equivariant map, unifying and generalizing different approaches followed by authors such as C. Kimberling…
The concept of center as an equivariant map and a proof of an analogue of the center conjecture for equifacetal simplices
Luis Felipe Prieto-Martínez
Several authors have remarked the convenience of understanding the different notions of center appearing in Geometry (centroid of a set of points, incenter of a triangle, center of…
The relation between symmetries and coincidence and collinearity of polygon centers and centers of multisets of points in the plane
Luis Felipe Prieto-Martínez
There are several remarkable points, defined for polygons and multisets of points in the plane, called centers (such as the centroid). To make possible their study, there exists a…
-gon centers and central lines
Marta Farré Puiggalí, Luis Felipe Prieto-Martínez
In this paper we provide a review of the concept of center of a -gon, generalizing the original idea given by C. Kimberling for triangles. We also generalize the concept of cent…
Circular arcs are the only analytic Jordan curves with an exterior power point
Luis Felipe Prieto-Martínez
In 1946, J. Rosenbaum proposed a family of problems asking how many power points are needed to ensure that the boundary of a given convex body is a disk. In this paper, we use…
Geometric continuity of plane curves in terms of Riordan matrices and an application to the F-chordal problem
Luis Felipe Prieto-Martínez
The first goal of this article is to provide an statement of the conditions for geometric continuity of order k, referred in the bibliography as beta-constraints, in terms of Riord…