The equation of the circle through three points
An algorithm to find the equation of the circle containing three (non-colinear) points.
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A circle problem
A recent tweet by @iwontoffendyou posed the following problem: with reference to the figure below, what is the radius of the orange circle, which is tangent to the $y$-axis, the unit circle and the curve $y = \sqrt{x}$?
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The Square Roots of Integers Visualized as Sharks Teeth
The Spiral of Theodorus (also known as the Snail of Pythogoras), illustrated below, is a well-known visualization of the square roots of the integers as the length of the hypotenuses of a sequence of right triangles, placed edge-to-edge. The Spiral of Theodorus [Pbroks13 at English …
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Cool DOIs in Python
A DOI (digital object identifier) is a persistent identifier used to uniquely identify various objects (usually documents or data sets). DOIs are typically presented as a link consisting of a proxy, a prefix and a suffix: for example: The proxy (here, https://doi.org/) is the location …
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Dyck paths and Catalan numbers
A Dyck path can be described as a sequence of horizontal steps for which, at each step a vertical step of or is taken subject to the constraints that the vertical coordinate never decreases below its initial value and the number of "up" and "down" …
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A QR code generator in Django
The following code is the views.py file for the make_qr app behind this QR code generator app. The qrcode Python package generates a Pillow Image object, which is encoded in base-64 for rendering in the template, saving the need for an intermediate PNG file.
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Deleting Gmail messages by label with the Google API
Google's suite of APIs and their Python bindings can be used to delete emails automatically, saving the hassle of navigating page after page of 100 emails at a time. Setting up a Developer project, configuring OAuth access etc. is described on the Google Developers page …
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Modular arithmetic on a circle
Inspired by David Richeson's applet on GeoGebra the Python script below plots the lines joining pairs of points, evenly spaced on the perimeter of a circle according to the following algorithm: label the points ; then join point to point . The line segments inside …
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The Goat Problem
A goat is tethered on the perimeter of a circular paddock of grass by a rope of length . What should be to allow the goat to graze on a maximum of half the area of the paddock? This is a famous problem in recreational …
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Maurer Roses
A Maurer rose is a shape formed by connecting the points on a rose defined in the polar coordinate system by for some positive integer, . The points to join are, in polar coordinates using degrees: For example, the Maurer rose defined by is: The …
