This work is about sets of points with integer pairwise distances (ideal sets) and Heron sets – ideal sets of points with integer area of its convex hull. It shows that any two-dimensional Heron set has an isometric copy in …

A self-avoiding walk (SAW) is a path that does not self-intersect, and the study of its properties leads to important applications in chemistry, biology and computer networks. We consider SAWs on a restricted square lattice with a finite height equal …

The work’s primary goal was to create a new and original solution to the Basel problem, the statement of which is to find the sum of reciprocals of squares of all positive integers. The prestented approach mainly aims for being …

Through studies of Danish text material and chosen passages from the Danish and Swedish Bible, it is investigated how the information theoretical entropy can be applied to quantify linguistic differences. It is shown that the relative entropy between Danish texts …

Natural disasters and complex disasters produce significant numbers of casualties that overload a region’s medical infrastructure. Field hospitals (FHs) help cope with this high influx of casualties. Often, they struggle with high patient arrival rates and limited personnel. This imbalance …

The aim of this project was to research a previously unresearched subject in combinatorial geometry – magic polyiamonds. To assist the research, multiple computer programs have been made by the authors, allowing for the collection of precise and accurate data …

Modular arirhmetic, aka arithmetic of clock, is a branch of mathematics studying remainders in division. Although it may seem unnecessary, it’s the central part of most bank or e-mail login systems and is a key idea of checksums that allow …

In this work figurate numbers on a plane and figurate numbers in a space were analyzed, as well as new figurate numbers (centered cubic numbers) were made. Common properties and features were revealed and the comparative analysis was made. When …

## Mathematics

## Sigma – Learning how computers learn

So-called “Artificial Intelligence” is now to be found in previously unimaginable places thanks to powerful computers becoming more affordable. With the project “Sigma – Learning how computers learn”, Florian Cäsar and Michael Plainer from the HTL Wels have set themselves …