# Blog

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## The Möbius function and the Mertens conjecture This blog post was inspired by Holly Krieger's video for Numberphile.

## Searching for pi-mnemonic strings in a text Piphilology comprises the creation and use of mnemonic techniques to remember a span of digits of the mathematical constant $\pi$. One famous technique, attributed to the physicist James Jeans uses the number of letters in each word of the sentence:

The quadtree data structure is a convenient way to store the location of arbitrarily-distributed points in two-dimensional space. Quadtrees are often used in image processing and collision detection.

## Processing UK Ordnance Survey terrain data The UK's Ordnance Survey mapping agency now makes its 50 m resolution elevation data freely-available through its online OpenData download service. This article uses Python, NumPy and Matplotlib to process and visualize these data without using a specialized GIS library.

## Visualizing uncertainties in plotted data The equation for the temperature-dependence of the diffusion of hydrogen in tungsten may be written in Arrhenius form: $$k = A\exp\left(-\frac{E}{T}\right) \quad \Rightarrow \; \ln k = \ln A - \frac{E}{T},$$ where the temperature, $T$, and activation energy, $E$, are expressed in eV and the pre-exponential Arrhenius parameter, $A$, and rate constant, $k$, take units of $\mathrm{m^2\,s^{-1}}$. From the study of Frauenfelder  the parameters $A$ and $E$ may be associated with uncertainties as follows: \begin{align*} A & = (4.1 \pm 0.5) \times 10^{-7}\;\mathrm{m^2\,s^{-1}}, \\ E &= 0.39 \pm 0.08 \;\mathrm{eV}. \end{align*} These uncertainties can be propagated to the expression for $\ln k$: $$\sigma_{\ln k} \approx \sqrt{ \left( \frac{\sigma_A}{A} \right)^2 + \left( \frac{\sigma_E}{T} \right)^2 }.$$ If we assume the uncertainty remains normally-distributed, Matplotlib's imshow function can be used to illustrate the Arrhenius equation for this data.