The University of Pretoria’s (UP) Department of Mathematics and Applied Mathematics recently enjoyed a two-day event to celebrate the International Day of Mathematics, which is observed worldwide on 14 March. Collaborating with the UP Maths Club and Blue Crane Space – a STEM-based student society – the department held an exhibition of various mathematical puzzles, arts and games on Hatfield campus.

The Tower of Hanoi puzzle was presented by Zerwick de Lange (BSc Physics) and Luan Naude (PhD Mathematics). The solution to this puzzle is typically presented in discrete mathematics and computational courses, as an example of the principle of mathematical induction and recursion.

The art gallery puzzle sought to determine the number of guards needed in an art gallery to observe the whole gallery. Gerlo Theron (BSc Mathematics) illustrated a simple yet elegant solution to the problem, known as the Art Gallery Theorem, which was proven by mathematician Steve Fisk. Theron showed two key ideas of Fisk’s proof: triangulation and the three-colouring argument from Graph Theory.

Eduard Plint (BSc Applied Mathematics) and Brendan Coetzee – BSc Physics (Hons) – demonstrated how mathematics can be used to model a physical problem, by presenting a mathematical model for a trebuchet. Instances of mathematics found in art forms were presented through the work of MC Escher, and the art of paper folding (origami). The mathematical aspects of origami have received a considerable amount of study with interesting applications, such as fitting the mirrors of the James Webb telescope into a rocket. Various optical illusions such as the Ames Room, the missing square and the infinite chocolate puzzles were presented as means to reason with (or not to reason with) geometrical figures.

Nicola Engelbrecht (BSc Applied Mathematics) shared interesting facts on the Möbius band, a classic example of non-orientable surfaces in mathematics, with her classmate Lourie Bosman (BSc Physics). The band can be easily formed by joining the ends of a strip of paper together with a half twist. Bosman and Engelbrecht showed variations of joining and cutting the band to get interesting shapes.

“What an amazing experience it was for us to come together and share our love and passion for mathematics,” Engelbrecht said.

The UP Maths Club, which was also involved in the celebration of the International Day of Mathematics in 2023, consists of students from various programmes, including mathematics/applied mathematics, statistics, physics and chemistry. Joining the celebration this year was the Blue Crane Space, which hosted the Pi recitation competition and the integration contest.

The celebration on 14 March took place at the Sci-Enza auditorium, with Ben Victor (MSc Mathematics) leading the first activity.

“I presented a mini-lecture on the Buffon Needle Problem and how its solution can be used to approximate the number π which we also did with the help of our enthusiastic audience members,” he said. “I think the celebration of the International Day of Mathematics was an outstanding success.”

Closing the event, Bosman presented a mini-lecture on the Bèzier curves. Named after French engineer Pierre Bèzier, the curves were used by him to design the bodywork of Renault cars. Bosman demonstrated how to obtain a simple Bèzier curve using pen and paper, and more sophisticated ones using graphing software.