DeepAI AI Chat
Log In Sign Up

Mechanization of Incidence Projective Geometry in Higher Dimensions, a Combinatorial Approach

by   Pascal Schreck, et al.
Université de Strasbourg

Several tools have been developed to enhance automation of theorem proving in the 2D plane. However, in 3D, only a few approaches have been studied, and to our knowledge, nothing has been done in higher dimensions. In this paper, we present a few examples of incidence geometry theorems in dimensions 3, 4, and 5. We then prove them with the help of a combinatorial prover based on matroid theory applied to geometry.


page 1

page 2

page 3

page 4


Algorithmic Fractal Dimensions in Geometric Measure Theory

The development of algorithmic fractal dimensions in this century has ha...

Uniform Brackets, Containers, and Combinatorial Macbeath Regions

We study the connections between three seemingly different combinatorial...

Electronic Geometry Textbook: A Geometric Textbook Knowledge Management System

Electronic Geometry Textbook is a knowledge management system that manag...

GraATP: A Graph Theoretic Approach for Automated Theorem Proving in Plane Geometry

Automated Theorem Proving (ATP) is an established branch of Artificial I...

Projection Theorems Using Effective Dimension

In this paper we use the theory of computing to study fractal dimensions...

GeoGebra Tools with Proof Capabilities

We report about significant enhancements of the complex algebraic geomet...

Can one design a geometry engine? On the (un)decidability of affine Euclidean geometries

We survey the status of decidabilty of the consequence relation in vario...