Result: Nonstandard geometric proofs
Title:
Nonstandard geometric proofs
Authors:
Source:
ADG 2000 : automated deduction in geometry (Zurich, 25-27 September 2000, revised papers)Lecture notes in computer science. :246-267
Publisher Information:
Berlin: Springer, 2001.
Publication Year:
2001
Physical Description:
print, 21 ref
Original Material:
INIST-CNRS
Subject Terms:
Computer science, Informatique, Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse mathématique, Mathematical analysis, Fonctions de plusieurs variables complexes et espaces analytiques, Several complex variables and analytic spaces, Sciences appliquees, Applied sciences, Informatique; automatique theorique; systemes, Computer science; control theory; systems, Intelligence artificielle, Artificial intelligence, Résolution de problèmes, jeux, Problem solving, game playing, Démonstration théorème, Theorem proving, Demostración teorema, Espace vectoriel, Vector space, Espacio vectorial, Géométrie algébrique, Algebraic geometry, Geometría algebraica, Théorie géométrique, Geometrical theory, Teoría geométrica, Transformation infinitésimale, Infinitesimal transformation, Transformación infinitesimal
Document Type:
Conference
Conference Paper
File Description:
text
Language:
English
Author Affiliations:
Division of Informatics - University of Edinburgh, 80 South Bridge, Edinburgh EH1 1HN, United Kingdom
ISSN:
0302-9743
Rights:
Copyright 2002 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Computer science; theoretical automation; systems
Mathematics
Mathematics
Accession Number:
edscal.14047822
Database:
PASCAL Archive
Further Information
This paper describes ongoing work in our formal investigation of some of the concepts and properties that arise when infinitesimal notions are introduced in a geometry theory. An algebraic geometry theory is developed in the theorem prover Isabelle using hyperreal vectors. We follow a strictly definitional approach and build our theory of vectors within the nonstandard analysis (NSA) framework developed in Isabelle. We show how this theory can be used to give intuitive, yet rigorous, nonstandard proofs of standard geometric theorems through the use of infinitesimal and infinite geometric quantities.