5 papers
Vectors and a half-disk of triangle shapes in Ionescu-Weitzenböck's inequality
Martin Celli
The aim of this note is to give two new conceptual proofs of Ionescu-Weitzenböck's inequality. The first one, which is a vector proof, provides us a geometric interpretation of the…
A dissection proof of the law of cosines, replacing Cuoco-McConnell's rectangles with congruent triangles
Martin Celli
Taking up the challenge McConnell laid down at the end of his proof of the law of cosines, we give a completely visual dissection proof of this theorem, which applies to any triang…
A proof of the butterfly theorem using the scale factor between the two wings
Martin Celli
We give a new proof of the butterfly theorem, based on the use of several expressions involving the scale factor between the two wings.
On polygonal relative equilibria in the N-vortex problem
Martin Celli, Ernesto A. Lacomba, Ernesto Pérez-Chavela
Helmholtz's equations provide the motion of a system of N vortices which describes a planar incompressible fluid with zero viscosity. A relative equilibrium is a particular solutio…
The central configurations of four masses x, -x, y, -y
Martin Celli
The configuration of a homothetic motion in the N-body problem is called a central configuration. In this paper, we prove that there are exactly three planar non-collinear central…