Rossby modes

A quick one containing the derivation of the Rossby modes of a 2d fluid on the surface of a sphere.

Another take at Zeno's paradox

Going back to this famous paradox, I talk about the concepts of motion, contradiction and dialetheism

The SIR model of infectious diseases

Reacting to the actuality of the coronavirus pandemic that we are currently living through, I present some simplified mathematical models used in epidemiology.

Some bell curves

I work out some of the properties of the Gaussian function from its generating differential equation including its first integral.

What growth means

A small explanation of the exponential function and its relation to the idea of perpetual growth.

The mathematics of Zeno's paradox

Pursuing an idea from an older post, I look at one of the simplest statements of Zeno's paradox and derive known results about infinite series of real numbers.

The waffle conundrum

I solve a relatively simple problem of geometry inspired by a culinary example from everyday life and find that the final answer has no closed analytical form. This illustrates how unexpected difficulties can emerge even in simple problems.

Toy model of a bouncing ball and Zeno's paradox

Starting from the common experience of hearing an object bouncing off the ground, I build a simplified model to compute the amount of energy being lost by the object along its course. This leads me to ponder about the possibility that the object could experience an infinite amount of rebounds in a finite amount of time.

Dimensional analysis

I give a short description of dimensional analysis and how it can be used to check the mathematics of computations in physics and also how it can be used to simplify the equations by getting rid of constant parameters.

Trajectories in the Schwarzschild space-time

Using the Riemann package presented in a previous post, one can easily perform basic computations in General Realtivity. In this post, I am going to show how it can be used to compute the geodesics of the Schwarzschild space-time.

An example in using the Riemann package

I have written a Mathematica package to perform basic computations in Riemannian geometry. In this post, I share an example of computation that this code can be used for and a link to the package containing the instructions to reproduce the computation presented here.

What is the distance to the horizon ?

I compute the distance of the horizon to an observer on the shore using trigonometry. I try to give a solution that is slightly more accurate than the classic way of the classic one based on Pythagora's theorem and compare the two results.

The rubber band theorem

I share a practical experiment of differential geometry by looking at two rubber bands on a table. This provides an opportunity to illustrate a theorem about the total curvature of closed curves.

The decimal point is ambiguous

A short post about the ambiguous nature of the decimal point. This illustrates how a number shouldn't be confused with its graphical representation.

Kinematic in a rotating reference frame

The equations that describe the dynamics of a point particle in space must be adapted when the motion is observed from an accelerated frame of reference. I give an illustration of this by considering the motion of a free particle relative to a frame rotating at a constant angular velocity around the origin of coordinates.

Geometry on a curved space

Euclid's axioms describe the geometry of shapes and curves in simple mathematical spaces which are called *flat*. When one considers more complex spaces, these axioms are no longer adequate. I illustrate this by looking at the special case where the mathematical space is a *two-sheet hyperboloid*.

What happens when you try to reach the speed of light ?

I talk about the mathematics describing what happens when a massive objects is accelerated at a steady rate and how it behaves when its velocity approaches that of light using the principles of special relativity.