Relating plane transformations with stereographic projection

Simple item page
dc.contributor.advisorNavarra-Madsen, Junalyn
dc.contributor.committeeMemberFalley, Brandi
dc.contributor.committeeMemberSmith, Shawnda
dc.creatorMcClintock, Patrick
dc.date.accessioned2023-02-22T21:37:35Z
dc.date.available2023-02-22T21:37:35Z
dc.date.created2022-12
dc.date.issued2022-12-01T06:00:00.000Z
dc.date.submittedDec-22
dc.date.updated2023-02-22T21:37:35Z
dc.description.abstractStereographic projection is a type of transformation mapping points on a sphere of dimension n+1 onto a plane of dimension n. It has properties such as continuity and preserving of certain angles which lend to exploring properties of the plane in relation to the sphere. Here stereographic projection is used as a method of drawing relationships between different two-dimensional spaces. Each of the complex plane, the split-complex plane, and the hyperbolic plane are examined in their relation to the Euclidean plane. First, Mobius transformations are considered on the complex plane. It is shown that every Mobius transformation can be represented via a movement of the sphere between two stereographic projections. Second, similar transformations are represented on the split-complex plane. Laguerre Transformations, analogous to Mobius transformations, explored with respect to split-complex numbers. Finally, a model of the hyperbolic plane is constructed using a pair of lateral projection and central projection.
dc.format.mimetypeapplication/pdf
dc.identifier.urihttps://hdl.handle.net/11274/14482
dc.language.isoEnglish
dc.subjectStereographic projection
dc.subjectCompactification
dc.subjectProjection
dc.subjectSplit-complex
dc.titleRelating plane transformations with stereographic projection
dc.typeThesis
dc.type.materialtext
thesis.degree.collegeCollege of Arts and Sciences
thesis.degree.departmentMathematics and Computer Sciences
thesis.degree.disciplineMathematics
thesis.degree.grantorTexas Woman's University
thesis.degree.nameMaster of Science

Files

Original bundle

Now showing 1 - 1 of 1
Thumbnail Image
Name:
MCCLINTOCK-PRIMARY-2022.pdf
Size:
526.18 KB
Format:
Adobe Portable Document Format
Download

License bundle

Now showing 1 - 2 of 2
No Thumbnail Available
Name:
proquest_license.txt
Size:
6.38 KB
Format:
Plain Text
Description:
Download
No Thumbnail Available
Name:
license.txt
Size:
2.06 KB
Format:
Plain Text
Description:
Download

Collections

Mathematics