The latest additions include several paintings and:. 1) Drawing in perspective: How simple objects appear when drawn accurately. This includes a section on how computer graphics software rotates an object, plus an account of nonlinear perspective using the map projections. A supporting article describes spherical triangles, 2) A simple question about a ladder leaning against a wall which leads to intriguing maths of ellipses and the astroid curve. 3) An attempt to find the largest sofa which can be manoeuvred round a 90 degree corner in a corridor (with animation). This is supported by statistics on the error in measuring the area of an arbitrary plane figure by counting the number of lattice points inside it. 4) Electrostatic field calculations relevant to electron lenses. Revisiting solutions of Laplace's equation in rectangular and cylindrical symmetry. My results for the conducting annulus may be new. 5 A short video of a chess game in CGI which I made in Blender from scratch. 6) two companion articles, one on Galois theory, the other on factoring polynomials, including those by Berlekamp and CantorZassenhaus, 7) More of my own paintings, plus an article on Great Paintings of Western art. Within the paintings page is a section of figure drawings. . 8) an investigation of the paradoxical rapid oscillations of a mandarin orange and other flatbottomed objects when tilted and released, Other topics "What makes a good tune?" I selected nearly 60 tunes from across the spectrum of Western music and dissected them to see what features they have in common. The article is here. There is also a subsidiary article about the shape of musical phrases and how mathematical curves can be fitted to these shapes. A related and ongoing project is to write a suite of computer programs which carry out some of the basic functions in creating 'classical' music. This is still work in progress, but I have placed here an account of progress so far. It uses none of the sophisticated methods of artificial intelligence, but instead takes a step by step approach to creating a sequence of major and minor triads, converting them to 4part harmony (like a hymn tune), then decorating the chords with rhythm and melody. Some while ago I added a section on matrices and their eigenvalues. That page hosts two articles, one on numerical algorithms for calculating eigenvalues and eigenvectors, and the other, recently completed, is on some elementary aspects of random matrices. Over the last 60 years random matricies have found application in many branches of number theory, nuclear physics, biological systems, phase transformations, and finance. On the Local History page is an article on Kepier water mill  it's about the longgone water corn mill at Kepier, Durham City, England, on the Local History page. There is another article about the CrossTown area of Knutsford, Cheshire. Acoustics of the violin family: Here is a long article describing how sound is radiated from vibrating objects. You can download it here. There is also my account of how we hear the sound of a violin. It describes how our ears detect sounds and how we can recognise pitch and loudness. There are some sound clips of how the pitch and tone of low notes on a viola are perceived by our ears, explaining the Paradox of The Missing Fundamental ! Other sections are:
