Geometry and Algebra

Title

Geometry and Algebra: Relating axioms for plane geometry to the field axioms

 Author

Bakker, David (TU Delft Electrical Engineering, Mathematics and Computer Science)

Contributor

Spandaw, J.G. (mentor) ORCID 0000-0001-8793-1622

 Degree granting institution

Delft University of Technology

 Programme

Applied Mathematics

 Date

2023-06-27

 Abstract

In 1908, the mathematician Felix Klein published a book Elementary Mathematics from an Advanced Standpoint: Geometry. This title aptly characterizes the focus of this thesis. This thesis introduces the axioms for Euclidean and projective plane geometry. Afterwards an arithmetic of lengths, based solely on these axioms, is constructed. By establishing a connection between the geometric axioms and the field axioms, it is demonstrated that these lengths form a field. It is shown that the original geometric plane is isomorphic to the Cartesian plane of lengths. Additionally, the thesis highlights the direct relation between two geometric propositions, Pappos’ theorem and Desargues’ theorem, and commutativity and associativity of the induced field of lengths.

 Subject

Axiomatic geometry
Coordinate geometry
Projective geometry
Hilbert's axioms

 To reference this document use:

http://resolver.tudelft.nl/uuid:0e71cdcb-260b-47f4-9f64-18c62f0c8036

 Part of collection

Student theses

 Document type

bachelor thesis

 Rights

© 2023 David Bakker
Files
PDF BakkerDavidBachelorThesis.pdf 5.88 MB
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