Arithmetic billiards at the National Jonk Fuerscher Contest

  • Faculty of Science, Technology and Medicine (FSTM)
    28 September 2023
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Prof. Antonella Perucca and doctoral student Flavio Perissinotto mentored young student Steve Mendeleev for his project “Edge Points in Three-Dimensional Arithmetic Billiards”. He participated in the National Jonk Fuerscher Contest and was awarded the prize to join the Taiwan International Science Fair in February 2024.

Steve shares his project.

What is your project about?

“I did my project about the investigation into 3D arithmetic billiards, and in particular focused on theorems I proved about the distribution of edge points — namely, I showed the edge points always are evenly spaced out and the spacing can be calculated with an explicit formula. I was offered the opportunity to research 3D arithmetic billiards by Prof. Perucca around June 2022 after attending one of her classes for the Course Defis. She sent me the 2D and provisional 3D billiards papers to read, and I afterwards had a few meetings with her and Flavio to narrow down what the scope of my investigation would be. I was also provided a Python script written by Sebastiano Tronto, which I further developed to measure additional features of 3D billiard simulations to collect data for my investigation. I then proved results analytically and compiled my results in a separate paper, which has been added to Prof. Perucca and Flavio’s provisional 3D billiards paper.”

How was the presentation of your project?

“At the actual competition, presenting the project itself consisted of making a slideshow covering what the project was, the purpose and its implications or potential applications, and the concrete mathematics I used in the proofs and investigation. I presented this slideshow to the jury, after which I was questioned by the jury, with some questions being about the applications and others about further extending the investigation to higher dimensions or other conditions. I also presented my project on a stand with a research poster and exchanged with visitors,  it was useful to meet other professional scientists and learn about relevant math topics I previously did not know about. Then came the award ceremony where fortunately every participant is awarded a prize in the form of entry to a separate international science competition. I was specifically awarded to travel to the Taiwan International Science Fair in February 2024.”

Prof. Antonella Perucca was very impressed by the work done: “It was very nice to work with Steve. We first explained all he needed to know about arithmetic billiards. Then we presented him with the results on edge points and their proofs, the exercise being to write the proofs down with all details. I was impressed by his very nice way of writing mathematics, which shows his mathematical maturity at an early age.”

Steve Mendeleev - 52nd National Jonk Fuerscher Contest