dc.contributor.author |
Moreno Martinez, Victor Manuel |
en |
dc.date.accessioned |
2009-06-09T23:13:35Z |
en |
dc.date.available |
2009-06-09T23:13:35Z |
en |
dc.date.issued |
2009-05 |
en |
dc.identifier.uri |
http://hdl.handle.net/10139/647 |
en |
dc.description.abstract |
The objective of this thesis is to create a concrete statement about the
existence of rational points in the unit square. We will use the following definition for a rational point: A rational point is defined as a point whose distances to the vertices of a geometric figure are all rational. Notice that a number theoretic rational point is a point (x, y) in an algebraic curve f(x, y) = 0 where x and y are rational. We will present a variety of methods to prove certain properties of these rational points. Finally we prove an equivalence between the non-existence of rational points on the edges of the unit square and the absence of integer roots for certain families of polynomials. |
en |
dc.language.iso |
en_US |
en |
dc.rights |
All rights reserved to author and California State University Channel Islands |
en |
dc.subject |
Rational points |
en |
dc.subject |
Unit square |
en |
dc.subject |
Tesselating the square with rational triangles |
en |
dc.subject |
Rational points in polygons |
en |
dc.subject |
Mathematics thesis |
en |
dc.title |
Rational Distances to the Corners of the Unit Square |
en |
dc.type |
Thesis |
en |