HEGL Illustrating Mathematics Seminar

Winter semester 2026-2027

Interactive Euclidean Geometry

During the Winter Semester 2026-2027, the HEGL Illustrating Mathematics Seminar will focus on Interactive Euclidean Geometry. The goal is to explore axiomatic Euclidean geometry and mathematical visualization on a computer to build interactive proofs of basic results in Euclid’s Elements.

A drawing illustrating the proof from Euclid's Elements that, given a line segment, one may construct an equilateral triangle that includes the segment as one of its sides: an equilateral triangle ΑΒΓ is made by drawing circles Δ and Ε centered on the points Α and Β, and taking one intersection of the circles as the third vertex of the triangle.

By Bcrowell. Source: Wikipedia. License: GPL.
  • Target audience: Bachelor students.
  • Language of instruction: English and German.
  • Supervised by: Florent Schaffhauser.
  • Time and place: Wednesdays 2:00-4:00 PM, in SR 5 (INF 205).
  • First meeting on 30.09.2026.

Organization

  • In the first half of the semester, the students are asked to give a seminar talk and produce a 3-page handout, both in English, as well a Geogebra picture. The material presented in these talks will be the basis for the project phase of the seminar.
  • In the second half of the semester, the students work on their visualization project, using the resources from the HEGL.
  • The students receive two grades: one for their talk and one for the project. The second grade is awarded on the basis of a final group presentation and the preparation of a blog post for the HEGL Blog. Each grade is worth 50% of the final grade of the seminar.
  • Attendance of all talks is mandatory.

References and schedule

Textbook

Textbook cover

Source: Springer Hochshultext.

The main reference for the seminar talks will be Part I from the book by Schwabhäuser et al. (1983), which is written in German. For the projects, we will use Geogebra or James Weber’s Interactive Euclide’s Elements Visualization.

Schedule

Schedule for the talks
Date Topic Speaker Chapters
30.09 Preliminary meeting
14.10 Tarski’s axioms Patryk Skiba Ch. 1
14.10 First results on betweenness and congruence Janne Tauner Ch. 2-5
21.10 Lines, half-lines and reflections through a point Sophia Scherer Ch. 6, 7
21.10 Right angles and reflections through a line Franziska Thiele Ch. 8, 10
28.10 Planes, half-planes and subspaces Luisa Furthmann Ch. 9
28.10 Congruent angles and orthogonality for subspaces Tung Anh Hoang Ch. 11
11.11 Parallelism and the theorems of Pappus and Desargues Ch. 12, 13
11.11 Project planning meeting
18.11 Project work
25.11 Status update meeting
02.12 Project work
09.12 Project work
16.12 Project work
13.01 Status update meeting
20.01 Final presentation

References

Schwabhäuser, Szmielew, and Tarski. 1983. Metamathematische Methoden in Der Geometrie. Springer-Verlag.