All blog posts - Page 2

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.

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.

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.

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.

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.

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

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.

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*.