Here you will find a few short excursions into mathematics - colorful and easy to understand - for students in grades 10 to 12/13 who are plagued by presentations. In each case, an introduction to a topic is presented, so there is room for independent work and in-depth study.
The buttons above the respective topic lead to the (forgotten?) prior knowledge that is necessary for understanding.
Circles roll on circles or straight lines, rods move in circles and rotate around their center, distances are extended, shifted, rotated, pendulums swing back and forth,... We find movement functions everywhere. Some of them are presented here: Cycloids, trochoids, spirals and the Möbius strip.
A reading sample from Ian Stewart's “Milestones in Mathematics” draws attention to how the introduction of coordinates contributed to the development of mathematics. Curves, such as the intersection of a cone, can now be represented by simple equations. The extension of the coordinate system to 3 dimensions by Fermat also made it possible to represent algebraic surfaces.
Coordinates on a sphere have become indispensable in mapping and navigation ... and what would economics and finance be without coordinates?
It is impossible to imagine mechanics without them.
This is an introduction to the topic of "Ordinary Differential Equations" for beginners.
Fractals, algorithmic plants, ... They can be found on many websites and sometimes enchant us with their beauty. It is not easy for beginners to understand how they are created. Therefore, the terms that appear again and again in this context are explained here in an easily understandable way.
As with isolines, points with the same properties are connected to represent 3-dimensional surfaces.
A differentiable function is the envelope of its tangents. Envelopes can also be found in art, e.g. in Naum Gabo's work.
If you have a quadratic function, it is easy to determine its zeros: The p-q formula, the quadratic addition and Vieta's theorem are well known. And if it works out “smoothly”, then you can also determine the points of intersection with the x-axis graphically.
This is not so easy with a non-linear, but continuously differentiable function: The Newton-Raphson method (Isaac Newton: 1642 - 1727, Joseph Raphson: 1648 - 1715) is a method that can be used to approximately determine the intersection points with the x-axis.
Heron of Alexandria (who probably lived in the first century AD) developed a method for determining square roots, which is presented on this page.
Heron's method for determining square roots is a special case of Newton's approximation method.
is a mapping in which the inside and outside of a circle are mapped onto each other.
If you like the pictures of 'Indra's Pearls' and want to program some yourself, you need to know a little about Moebius transformations and iterated mappings in the field of complex numbers.