• A test of OpenJSCAD

    calendar Sep 15, 2018 · 1 min read · CAD  ·
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    Here's an example of a coloured tetrahedron:

    <div oncontextmenu="return false;"
     id="viewerContext"
     style = "width:640px;height:470px;"
     design-url="tetrahedron.jscad"></div>

    <div id="tail" …

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  • The power of two irrational numbers being rational

    calendar Sep 15, 2018 · 1 min read · mathematics  ·
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    There's a celebrated elementary result which claims that:

    There are irrational numbers \(x\) and \(y\) for which \(x^y\) is rational.

    The standard proof goes like this. Now, we know that \(\sqrt{2}\) is irrational, so let's consider \(r=\sqrt{2}^\sqrt{2}\). Either \(r\) is rational, or it is not. If it is rational, …


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  • Wrestling with Docker

    calendar Sep 15, 2018 · 4 min read  ·
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    For years I have been running a blog and other web apps on a VPS running Ubuntu 14.04 and Apache - a standard LAMP system. However, after experimenting with some apps - temporarily installing them and testing them, only to discard them, the system was becoming a total mess. Worst of all, various MySQL files were …
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  • Householder's methods

    calendar Sep 9, 2018 · 4 min read · mathematics algebra  ·
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    These are a class of root-finding methods; that is, for the numerical solution of a single nonlinear equation, developed by Alston Scott Householder in 1970. They may be considered a generalisation of the well known Newton-Raphson method (also known more simply as Newton's method) defined by

    \[ x\leftarrow …


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  • The Joukowsky Transform

    calendar Aug 24, 2018 · 1 min read · mathematics geometry jsxgraph  ·
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    The Joukowksy Transform is an elegant and simple way to create an airfoil shape.

    Let \(C\) be a circle in the complex plane that passes through the point \(z=1\) and encompasses the point \(z=-1\). The transform is defined as

    \[ \zeta=z+\frac{1}{z}. \]

    We can explore the transform by looking at the circles centred at …


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  • Double Damask

    calendar Apr 27, 2018 · 5 min read · humour  ·
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    This was a comedy sketch initially performed in the revue "Clowns in Clover" which had its first performance at the Adelphi Theatre in London on December 1, 1927. This particular sketch was written by Dion Titheradge and starred the inimitable Cicely Courtneidge as the annoyed customer Mrs Spooner. It has …
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  • Graphs of Eggs

    calendar Apr 20, 2018 · 2 min read · geometry jsxgraph  ·
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    I recently came across some nice material on John Cook's blog about equations that described eggs.

    It turns out there are vast number of equations whose graphs are egg-shaped: that is, basically ellipse shape, but with one end "rounder" than the other.

    You can see lots at Jürgen Köller's Mathematische …


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  • Exploring JSXGraph

    calendar Apr 14, 2018 · 2 min read · jsxgraph  ·
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    JSXGraph is a graphics package deveoped in Javascript, and which seems to be tailor-made for a static blog such as this. It consists of only two files: the javascript file itself, and an accompanying css file, which you can download. Alternaively you can simply link to the online files at the Javascript content …
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  • The trinomial theorem

    calendar Apr 5, 2018 · 2 min read · mathematics algebra  ·
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    When I was teaching the binomial theorem (or, to be more accurate, the binomial expansion) to my long-suffering students, one of them asked me if there was a trinomial theorem. Well, of course there is, although in fact expanding sums of greater than two terms is generally not classed as a theorem described by the …
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  • Playing with Hugo

    calendar Apr 3, 2018 · 3 min read · hugo org  ·
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    I've been using wordpress as my blogging platform since I first started, about 10 years ago. (In fact the first post I can find is dated March 30, 2008.) I chose wordpress.com back then because it was (a) free, and (b) supported mathematics through a version (or subset) of LaTeX. As I have used LaTeX extensively for …
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