DeepAI AI Chat
Log In Sign Up

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

01/03/2022
by   Pascal Schreck, et al.
Université de Strasbourg
0

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.

READ FULL TEXT

page 1

page 2

page 3

page 4

07/28/2020

Algorithmic Fractal Dimensions in Geometric Measure Theory

The development of algorithmic fractal dimensions in this century has ha...
11/19/2021

Uniform Brackets, Containers, and Combinatorial Macbeath Regions

We study the connections between three seemingly different combinatorial...
05/01/2010

Electronic Geometry Textbook: A Geometric Textbook Knowledge Management System

Electronic Geometry Textbook is a knowledge management system that manag...
12/18/2014

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

Automated Theorem Proving (ATP) is an established branch of Artificial I...
11/06/2017

Projection Theorems Using Effective Dimension

In this paper we use the theory of computing to study fractal dimensions...
03/03/2016

GeoGebra Tools with Proof Capabilities

We report about significant enhancements of the complex algebraic geomet...
12/20/2017

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...