1,120 research outputs found
Angle Bisectors of a Triangle in Lorentzian Plane
In Lorentzian geometry, limited definition of angles restricts the use of
angle bisectors in study of triangles. This paper redefines angle bisectors so
that they can be used to study attributes of triangles. Using the new
definition, this paper investigates the existence of the incenter and the
isogonal conjugate of a triangle in Lorentzian plane.Comment: 15 pages, 7 figure
A 1-parameter family of spherical CR uniformizations of the figure eight knot complement
We describe a simple fundamental domain for the holonomy group of the
boundary unipotent spherical CR uniformization of the figure eight knot
complement, and deduce that small deformations of that holonomy group (such
that the boundary holonomy remains parabolic) also give a uniformization of the
figure eight knot complement. Finally, we construct an explicit 1-parameter
family of deformations of the boundary unipotent holonomy group such that the
boundary holonomy is twist-parabolic. For small values of the twist of these
parabolic elements, this produces a 1-parameter family of pairwise
non-conjugate spherical CR uniformizations of the figure eight knot complement
Skeletal Rigidity of Phylogenetic Trees
Motivated by geometric origami and the straight skeleton construction, we
outline a map between spaces of phylogenetic trees and spaces of planar
polygons. The limitations of this map is studied through explicit examples,
culminating in proving a structural rigidity result.Comment: 17 pages, 12 figure
Reasoning By Contradiction in Dynamic Geometry
This paper addresses contributions that dynamic geometry systems (DGSs) may give in reasoning by contradiction in geometry. We present analyses of three excerpts of students’ work and use the notion of pseudo object, elaborated from previous research, to show some specificities of DGS in constructing proof by contradiction. In particular, we support the claim that a DGS can offer “guidance” in the solver’s development of an indirect argument thanks to the potential it offers of both constructing certain properties robustly, and of helping the solver perceive pseudo objects
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