# Sofia Killander: Projektiv geometri

BSc thesis presentation

**Time: **
Tue 2020-06-16 13.00 - 14.00

**Location: **
Zoom, meeting ID: 616 1140 9519

**Participating: **
Sofia Killander

**Supervisor: **
Torbjörn Tambour

### Abstract

This report focuses on the basics of projective geometry and the relationship between art and mathematics. We will learn how projective geometry grew into a unique part of mathematics and who the men who introduced, practised and founded it were. The connection between geometry and art is of great importance in this report, but also natural phenomenon such as shadows and reflections of the sun will be mathematically viewed. We will discuss the differences between Euclidean and projective geometry and observe where they differ. The report includes different mathematical techniques practiced by artists and architects, where for instance central projection, vanishing points and line and how to draw a checkered floor are included. Desargues theorem will be formulated and proved in three dimensions. The last chapter focuses on the dual relation between points and lines as well as the duality within geometric figures.

The report is written mainly with knowledge from “Åtta kapitel om geometri” written by Anders Tengstrand and “Centralprojektion och perspektiv” written by Torbjörn Tambour. All figures are drawn by the author of this report, Sofia Killander, in Google docs. The report is written in Swedish.