Today’s entry is a Theorem of the Day: The Robin-Lagarias Theorem: Let $H_n$ denote the n-th harmonic number $\sum_{i=1}^n \frac{1}{i}$ , and let $\sigma(n)$ denote the divisor function $\sum_{d \vert n} d$. Then the Riemann Hypothesis is equivalent to the statement that, for $n \geq 1$, $\sigma(n) \leq H_n + \ln(H_n) e^{H_n}$ . While this…

The Gingerbreadman Map is a two-dimensional piecewise linear map, defined by: \begin{align} x_{n+1} &= 1 – y_n + \lvert x_n \rvert \\ y_{n+1} &= x_n \end{align} The region in which the map is chaotic looks like a gingerbread man! In true festive spirit, one blogger has baked some cookies in the shape of the gingerbread…

Describing itself as ‘the Sierpinski Triangle page to end all Sierpinski Triangle pages‘, this webpage certainly contains an amazing amount of information, diagrams and code to study and explore the well-known equilateral fractal. It goes on forever! (The fractal, not the page – although it does seem like it might never end). This is part of the…

  Today’s advent calendar window is covered in snowflakes! These snowflakes aren’t your usual sort, however – they’re made up of thousands of toothpicks arranged into E shapes. Hey, nobody mixes metaphors like mathematicians. The image above shows 1,124 E-shapes arranged rather artfully. 1,124 is the 32nd entry of the sequence A161330, which lists how many shapes…

This is part of the Aperiodical Advent Calendar. We’ll be posting a new surprise for you each morning until Christmas!

Ever wanted to look up a number and find out all kinds of things about it (like, if you’re making a mathematical advent calendar and want interesting facts about the date each day)? No longer do you have to sift through all the tedious non-maths facts you get if you look up a number on…