## Elephant Delta Day 3 – Dr Alice Hui from The University of KwaZulu-Natal on Projective geometry as an undergraduate course: a tour of the three worlds of mathematics

Blogging from The Tenth Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics

Dr Alice Hui from The University of KwaZulu-Natal.

Projective geometry as an undergraduate course: A tour of the three worlds of mathematics.

Attempt to persuade the audience to have projective geometry as an undegraduate course.

**What is Projective Geometry?**

Projective geometry describes objects as they appear, rather than as they are.

Two sides of a train track are parallel but look interest in the far end.

Taken from https://plus.maths.org/content/sites/plus.maths.org/files/features/projective/tracks1_small.jpg

- Advantages of having projective geometry as an undergraduate course
- An axiomatic approach to study geometry
- A projective plane satisfies three axioms.
- Can allow students to study geometry using an axiomatic approach.
- Comparison to other axiomatic formulations that may be taught in undergraduate courses:
- We use axioms to study natural numbers, real numbers, group, ring, field, vector space, set theory. They are not geometric.
- Euclid’s Element is not rigorous in modern sense.

- An axiomatic approach to study geometry