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A goat is tethered on the perimeter of a circular paddock of grass by a rope of length $r$. What should $r$ be to allow the goat to graze on a maximum of half the area of the paddock?

A Maurer rose is a shape formed by connecting the points on a rose defined in the polar coordinate system by $r = \sin(n\theta)$ for some positive integer, $n$. The points to join are, in polar coordinates using degrees:

The following code identifies a QR code in a provided image and plays John Conway's Game of Life with it. It uses OpenCV (for image recognition and QR code detection), along with SciPy, NumPy and Matplotlib. If you don't have them, they can be installed with

The Weierstrass function, named after the German mathematician Karl Weierstrass (1815 – 1897) is a real-valued function that is continuous everywhere but nowhere differentiable. It is usually expressed as a Fourier series:

The Digital Technology Group (DTG) at Cambridge University has been recording the weather from the roof of their building since 1995. The complete data are available to download in CSV format from the DTG website as the file weather-raw.csv.