The content of these presentations and the article is mathematics itself. They are arranged by complexity, from simpler to more complex. Middle school math education, or going through the first two circles of the Understanding and Doing Math books series, is enough to follow these, apart from the last article. To fully follow the last article would require going through all four Math circles, although I think it is worth reading the whole article and skipping the mathematical parts that are too demanding for the reader All presentations are in Croatian. I will translate them into English in a due course.
In the presentation Children, don’t be afraid, giant ants cannot exist, I show how the simple notion of similarity can be used to understand many phenomena around us, why there are no giant ants, among others.
In the presentation Circle area, circle circumference and number Pi, I show how formulas for the area and perimeter of a circle can be derived using the notion of similarity and the idea of linear approximation.
In the presentation A parable in mathematics and physics (but not literature), the definition of a parabola is motivated by one optical problem and its equation is derived from that definition. Starting from Galileo’s law of free fall and Galileo’s principle of relativity, it has been shown that the trajectory of a projectile is precisely a parabola.
The aim of the presentation Geometry on the Earth’s surface is to relativize Euclidean geometry to the student by showing him that there are different geometries and leading him to ask what the geometry of the real world is. At the same time, the student will get acquainted with the way we really orient ourselves and move around our planet.
The article The forgotten mathematical history of the modern computer presents the mathematical history of the modern computer, about which little is known outside the mathematical profession. This history is very important for understanding the mathematical and logical ideas that underlie computing and the emergence of the modern computer, as well as for understanding the important role of mathematics in computer science. Computer science is not just engineering, as is commonly thought, but engineering and mathematics are equally present in it.