Abstract
dc:description.abstractOne of the marvelous phenomena of coordinate geometry is the equivalence of Desargues' Theorem to the presence of an underlying division ring in a projective plane. Supplementing this correspondence is the general theory of intersection theorems, which, restricted to desarguian projective planes P, corresponds precisely to the theory of integral rational identities, restricted to division rings D. The first chapter of this paper introduces projective planes, develops the concept of an intersection theorem, and expounds upon the Theorem of Desargues; the discussion culminates with a proof of the desarguian phenomenon in the second chapter. The third chapter characterizes the automorphisms of P and introduces the theory of polynomial identities; the fourth chapter expands this discussion to rational identities and cements the ``dictionary''. The last section describes a measure of complexity for these intersection theorems, and the paper concludes with a curious spawn of the correspondence.
Degree
thesis:*- Name thesis:degree_name
- Master of Science
- Level thesis:degree_level
- masters
- Discipline thesis:degree_discipline
- Mathematics
- Department dc:contributor.department
- Mathematics
- Grantor dc:publisher
- Virginia Tech
- Year dc:date.issued
- 2005
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Brunson, Jason Cornelius
- Chair dc:contributor.committeechair
-
- Farkas, Daniel R.
- Committee members dc:contributor.committeemember
-
- Brown, Ezra A.
- Shimozono, Mark M.
Subjects
dc:subject × 3Rights
dc:rights- Statement dc:rights
-
- In Copyright
- Licence dc:rights.uri
Identifiers
dc:identifier.*- Dc Identifier Other
- etd-05102005-144432
- OAI identifier oai:identifier
- oai:vtechworks.lib.vt.edu:10919/32498