Visuals in Special Relativity

This animation illustrates how a forward-moving cube with various speeds looks to a static observer. We see that at half the speed of light the cube already looks tilted, however, the back remains invisible to the observer. At 90% of the speed of light, the backside gets visible to the observer since the cube is moving faster than the component of the light ray pointing to the observer, hence the path is free quick enough.

Mnemonic to convert between Celsius °C and Fahrenheit °F

Between 0°C and 100°C are 180°F. This allows for a nice mnemonic to convert between those units using an angle as a guide for °F.

Bohmian Mechanics

Bohmian Mechanics is a popular Interpretation of Quantum Mechanics among Mathematical Physicists. The reason might be the axiomatic nature of the theory: The Schrödinger Equation is accompanied by a system of ODEs, more specifically equations of motion for every particle. Those are constructed via the wave function. The animation above shows the Bohmian trajectories of electrons in a double split experiment. The result is a quite known interference pattern.

How far until the horizon?

Assuming a non-flat earth, how far can you look until you catch up to the horizon?

Slope without Derivative / Limits?!

Since the introduction to limits in calculus might be confusing, especially the concept of limits to calculate the slope of a function, it is a nice treat to see that the same formula can be obtained in other ways. Here is an example of how one can get the same formula for the derivative of a parabola utilizing the convex/concave property that the tangent will never intersect the function again! I find this really useful in education and teaching!

Closed Knight's tour Mnemonic!

This is one of 26,534,728,821,064 closed, directed knight's tours (Hamiltonian Path), that is, the knight visits every square once and only once. Remembering the four colored figures allows you to complete a tour from any square of the board!

Riemann Sum Animation!

A small animation of a middle Riemann sum to integrate a function. In this example, one can see the error becoming lower with each increase of partitions!

Mathematical Valentine's Day!

Happy Valentines Day! Two functions merge to one heart with a very special area.