Monthly Archives: September 2012

Second and third chapters

The second and third chapters of Mathematical Olympiad Dark Arts can now be downloaded for public review. Preface Combinatorics I (enumerative and geometrical combinatorics) Linear algebra Combinatorics II (graph theory) Polynomials Sequences Inequalities Projective geometry Complex numbers Triangle geometry Areal coordinates The … Continue reading

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Big Mandelbrots

The Mandelbrot set, as you’re probably aware, is the set of points c in the complex plane such that iterating f(z) = z² + c repeatedly doesn’t escape to infinity. By invoking the triangle inequality, it can be shown that a point … Continue reading

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Dürer’s square

In Albrecht Dürer’s 1514 engraving Melancolia I, there is a famous 4×4 magic square. In addition to the rows, columns and main diagonals summing to 34, so do various other arrangements such as the quadrants and four corners. We can transform this into an … Continue reading

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There have been several recent items of news, either related to or inspired by the recent postings on Complex Projective 4-Space. Rather than mention them separately, I have collected them in this ‘digest’ format. Jigcypher solved I received an anonymous e-mail … Continue reading

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MODA ready for review

After several rounds of editing and peer-review, I have decided that my book, Mathematical Olympiad Dark Arts, has reached a point where it is suitable for public review. Rather than upload the entire 176-page document in its entirety, I shall … Continue reading

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Closed-form bijections

One of the qualities of a quintessential British mathematician is the ability to invent crazy and contrived functions to satisfy particular properties. For instance, John Conway’s base-13 function was designed as a counter-example to the converse of the Intermediate Value … Continue reading

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Activities with golden rhombi

For this post, I’ve decided to do something different. Instead of the usual mathematical monologue, this is a more of a hands-on activity. It is centred around the golden rhombus, which is so named because the ratio of the diagonals is … Continue reading

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