Page 411 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 411
MATHEMATICS IN EDUCATION (MS-19)
Five Mathematicians from MacTutor History of Mathematics
Marko Razpet, marko.razpet@guest.arnes.si
Retired, Slovenia
Coauthors: Izidor Hafner, Nada Razpet
We exhibit posters describing lives and work of Jurij Vega, Franc Mocˇnik, Josip Plemelj, Ivo
Lah, and Ivan Vidav. These five Slovenian mathematicians that are covered by MacTutor His-
tory of Mathematics significantly influenced the development of mathematics in Slovenia.
Graph Theory Between The World Wars
Antonín Slavík, slavik@karlin.mff.cuni.cz
Charles University, Prague, Czech Republic
We focus on the development of graph theory in the interwar period. In the 1930s, there were
still many mathematicians who did not regard graph theory as a serious discipline, owing partly
to the fact that many results in this field were originally inspired by problems of recreational
mathematics. However, the publication of the first textbook of graph theory in 1936, which pre-
sented it as a completely rigorous discipline with applications in linear algebra and set theory,
helped to change this attitude. Meanwhile, some important results that are now classified as
belonging to graph theory were formulated in the language of topological structures. Finally,
one should not forget that numerous developments in graph theory grew out of purely practi-
cal problems, such as the construction of electricity networks, or the enumeration of chemical
compounds.
Software generation of images using mathematics
Bogdan Soban, bogdan@soban-art.com
retired, Slovenia
I use my software developed in the Visual Basic programming language to generate images.
An algorithmic approach is used, which enables a high level of diversity of results with rel-
atively short but mathematically supported software solutions. At each point of the image, a
programming algorithm is executed, consisting of mathematical formulas that enter pieces of
information, which are constant for the current cycle (genetic code) and variables generated by
the process itself. The result of the calculation is the color of the point or the position where
to remove the color from the color palette, which plays the role of a key variable. The image
coordinate system, the Cartesian and polar coordinate system, and the logic of the complex
plane are used to control the image. The whole process is supported by a time-determined
random number generator, which supplies the system with random values of various parame-
ters and thus ensures unpredictability and non-repetition of the results. From the viewpoint of
mathematics, the following notions appear in the algorithms: complex algebraic expressions,
trigonometric and logarithmic functions, plane geometry, iterations and recursions, determi-
nation of random numbers in areas, conversion of coordinates between different coordinate
systems, control of stochastic motion of a point in plane and space, circular and spiral move-
ments, computation with complex numbers, original formulas for various calculations, number
409
Five Mathematicians from MacTutor History of Mathematics
Marko Razpet, marko.razpet@guest.arnes.si
Retired, Slovenia
Coauthors: Izidor Hafner, Nada Razpet
We exhibit posters describing lives and work of Jurij Vega, Franc Mocˇnik, Josip Plemelj, Ivo
Lah, and Ivan Vidav. These five Slovenian mathematicians that are covered by MacTutor His-
tory of Mathematics significantly influenced the development of mathematics in Slovenia.
Graph Theory Between The World Wars
Antonín Slavík, slavik@karlin.mff.cuni.cz
Charles University, Prague, Czech Republic
We focus on the development of graph theory in the interwar period. In the 1930s, there were
still many mathematicians who did not regard graph theory as a serious discipline, owing partly
to the fact that many results in this field were originally inspired by problems of recreational
mathematics. However, the publication of the first textbook of graph theory in 1936, which pre-
sented it as a completely rigorous discipline with applications in linear algebra and set theory,
helped to change this attitude. Meanwhile, some important results that are now classified as
belonging to graph theory were formulated in the language of topological structures. Finally,
one should not forget that numerous developments in graph theory grew out of purely practi-
cal problems, such as the construction of electricity networks, or the enumeration of chemical
compounds.
Software generation of images using mathematics
Bogdan Soban, bogdan@soban-art.com
retired, Slovenia
I use my software developed in the Visual Basic programming language to generate images.
An algorithmic approach is used, which enables a high level of diversity of results with rel-
atively short but mathematically supported software solutions. At each point of the image, a
programming algorithm is executed, consisting of mathematical formulas that enter pieces of
information, which are constant for the current cycle (genetic code) and variables generated by
the process itself. The result of the calculation is the color of the point or the position where
to remove the color from the color palette, which plays the role of a key variable. The image
coordinate system, the Cartesian and polar coordinate system, and the logic of the complex
plane are used to control the image. The whole process is supported by a time-determined
random number generator, which supplies the system with random values of various parame-
ters and thus ensures unpredictability and non-repetition of the results. From the viewpoint of
mathematics, the following notions appear in the algorithms: complex algebraic expressions,
trigonometric and logarithmic functions, plane geometry, iterations and recursions, determi-
nation of random numbers in areas, conversion of coordinates between different coordinate
systems, control of stochastic motion of a point in plane and space, circular and spiral move-
ments, computation with complex numbers, original formulas for various calculations, number
409
