A blog of Python-related topics and code.

The mildly controversial geocoding system What3words encodes the geographic coordinates of a location (to a resolution of 3 m) on the Earth's surface into three dictionary words, through some proprietary algorithm. The idea is that human's find it easier to remember and communicate these words than the sequence of digits that makes up the corresponding latitude and longitude. For example, the Victoria Memorial in front of Buckingham Palace in London is located at (51.50187, -0.14063) in decimal latitude, longitude coordinates, but simply `using.woods.laws`

in the language of What3words.

The magnetic field due to a magnetic dipole moment, $\boldsymbol{m}$ at a point $\boldsymbol{r}$ relative to it may be written $$ \boldsymbol{B}(\boldsymbol{r}) = \frac{\mu_0}{4\pi r^3}[3\boldsymbol{\hat{r}(\boldsymbol{\hat{r}} \cdot \boldsymbol{m}) - \boldsymbol{m}}], $$ where $\mu_0$ is the vacuum permeability. In geomagnetism, it is usual to write the radial and angular components of $\boldsymbol{B}$ as: $$ \begin{align*} B_r & = -2B_0\left(\frac{R_\mathrm{E}}{r}\right)^3\cos\theta, \\ B_\theta & = -B_0\left(\frac{R_\mathrm{E}}{r}\right)^3\sin\theta, \\ B_\phi &= 0, \end{align*} $$ where $\theta$ is polar (colatitude) angle (relative to the magnetic North pole), $\phi$ is the azimuthal angle (longitude), and $R_\mathrm{E}$ is the Earth's radius, about 6370 km. See below for a derivation of these formulae.

This Jupyter Notebook can be downloaded and viewed at my GitHub repository.

The Earth Impact Database is a collection of images, publications and abstracts that provides information about confirmed impact structures for the scientific community. It is hosted at the Planetary and Space Science Centre (PASSC) of the University of New Brunswick.

Matplotlib isn't the obvious choice for depicting the *Star Wars* opening crawl, but that isn't a reason not to try: