GEOMETRIC CONSTRUCTIONS

Lang, Origami and Geometric Constructions Origami and Geometric Constructions 1 Lang, Origami and Geometric Constructions Introduction

By Robert J. Lang Copyright ©1996–2015. All rights reserved. Introduction ................................................................................................................................... 3 Preliminaries and Definitions ...................................................................................................... 3 Binary Divisions ........................................

Lang, Origami and Geometric Constructions Origami and Geometric Constructions Introduction

Tropical plane geometric constructions

In this article we give a general method to compute sets of algebraic curves with prescribed incidence relations and tropicalizations. It generalizes the geometric constructions presented in Tabera, 2005 to the non linear case.

Elegant Geometric Constructions

After a half century of curriculum reforms, it is fair to say that mathematicians and educators have come full circle in recognizing the relevance of euclidean geometry in the teaching and learning of mathematics. For example, in [15], J. E. McClure reasoned that “Euclidean geometry is the only mathematical subject that is really in a position to provide the grounds for its own axiomatic proced...

Axiomatizing geometric constructions

In this survey paper, we present several results linking quantifier-free axiomatizations of various Euclidean and hyperbolic geometries in languages without relation symbols to geometric constructibility theorems. Several fragments of Euclidean and hyperbolic geometries turn out to be naturally occurring only when we ask for the universal theory of the standard plane (Euclidean or hyperbolic), ...