Title: The Foundations of Geometry

Description

• exposé
• cours - matière potentielle : lectures on euclidean geometry

Project Gutenberg's The Foundations of Geometry, by David Hilbert This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at Title: The Foundations of Geometry Author: David Hilbert Release Date: December 23, 2005 [EBook _17384] Language: English Character set encoding: TeX *** START OF THIS PROJECT GUTENBERG EBOOK FOUNDATIONS OF GEOMETRY *** Produced by Joshua Hutchinson, Roger Frank, David Starner and the Online

• hilbert as a course of lectures on euclidean geometry
• criterion for the possibility of a geometrical construction by means
• demonstration for plane geometry by aid of the axioms of congruence
• geometry by david hilbert
• means of the theorems
• axioms
• geometry
• straight line
• space
• points

Sujets

• Exposé
• Hutchinson
• University of Göttingen
• Introduction
• Geometry
• Straight

Informations

• Publié par: unnu
• Nombre de lectures: 14
• Langue: English

Extrait

FUNDAMENTALS

Program

 Introduction to matrix algebra  Symmetry in nature and in human life

BASIC CONCEPTS

 Affine spaces vs. vector spaces  Mappings: affine and Euclidean; isometries and symmetry operations  Sets; homomorphisms, isomorphisms, automorphisms  Introduction to group theory: abstract groups, subgroups, cosets

CRYSTALLOGRAPHY IN DIRECT SPACE

 Periodic structure of the crystalline matter  Crystal lattice vs. crystal pattern and crystal structure  Symmetry directions in a lattice  Unit cells: primitive cells, multiple cells, conventional cells in 2D and 3D  Crystal families  Symmetry groups and types of symmetry in direct space o morphological symmetry o symmetry of physical properties o symmetry of lattices o symmetry of the unit cell content o symmetry of crystallographic patterns o HermannMauguin symbols for point groups  lattice systems  Crystal systems  Stereographic projection and the morphology of crystals  Types of crystallographic point groups through the stereographic projection  Generation of space groups. Symmetry operations with and without a glide component. HermannMauguin symbols for space groups  Orthogonal projections of space groups. General and special positions, sitesymmetry groups, crystallographic orbits  Introduction to crystallographic calculations through matrix algebra. Abstract groups, subgroups, cosets  Short introduction to the subgroups and supergroups of space groups  Exercises on the space group diagrams from Volume A of theInternational Tables for Crystallography

PHYSICS OF DIFFRACTION AND CRYSTALLOGRAPHIC IN RECIPROCAL SPACE

 Interaction of Xrays with crystalline matter