Author Archives: apgoucher

Hyperbolic Minecraft

Posted on September 12, 2014 by apgoucher

(Firstly, this is a test to see whether WordPress is configured to automatically link to cp4space posts as tweets from apgox. Hopefully it will succeed.) Yesterday, I received a rather interesting e-mail from Tim Hutton, lead developer of the reaction-diffusion … Continue reading →

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First female Fields medallist

Posted on August 12, 2014 by apgoucher

Tomorrow, this year’s Fields medals were awarded*. The four recipients of this prestigious quadrennial accolade have made profound advancements in their respective areas of mathematics, specifically: Artur Avila has revolutionised the study of dynamical systems, proving many hitherto open conjectures … Continue reading →

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How to do geometry properly

Posted on August 10, 2014 by apgoucher

For literally thousands of years, people have been writing books about elementary geometry. Many of these, such as Bradley and Gardiner’s Plane Euclidean Geometry, are concerned with solving problems in Euclidean geometry. They are subsequently bought by many adolescents intending to … Continue reading →

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I’m still alive

Posted on July 23, 2014 by apgoucher

So, there hasn’t been a cp4space post for over a fortnight now. I’ll now attempt to excuse this massive lapse, and hopefully convince you that what I’ve been doing in the meantime is still somewhat worthwhile. Amongst other things, I … Continue reading →

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If sunflowers were square

Posted on July 6, 2014 by apgoucher

What did Alan Turing ever do for us? Answering this question is much more subtle than one would initially imagine. He has shaped the world in at least three diverse waves of influence, which despite being apparently disparate are inextricably linked both historically … Continue reading →

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Applications of quaternions

Posted on June 30, 2014 by apgoucher

Quaternions were discovered by Sir William Rowan Hamilton in a flash of inspiration as he crossed Brougham Bridge, inscribing the following relations into one of the stones: i² = j² = k² = ijk = −1 Specifically, a quaternion is a number of the form q … Continue reading →

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Cipher 70: Wild goose chase

Posted on June 23, 2014 by apgoucher

Once again it is Cipher Tuesday, and this time I actually have a cipher to release: 1. Frg hc n purffobneq va gur fgnegvat cbfvgvba. 2. Ba n cvrpr bs 90tfz N4 cncre, qenj gur Qlaxva qvntenz bs gur fdhner … Continue reading →

Posted in Ciphers | 20 Comments

Cavalieri’s principle

Posted on June 13, 2014 by apgoucher

Disclaimer (mainly to Marcus du Sautoy): The Ancient Greeks did not invent integration, and whilst I shall use Ancient Greek principles of mensuration to justify Riemann and Lebesgue integration, the Ancient Greeks did no such thing. Finding volumes of cones … Continue reading →

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Cipher 69: A void

Posted on June 7, 2014 by apgoucher

Before this week’s cipher, I have a few late items of news: Professor Stephen Hawking has recently committed a Eugenia Cheng, publishing a formula for the perfect penalty shootout. There is a biographical movie about Srinivasa Ramanujan, unsurprisingly entitled Ramanujan, … Continue reading →

Posted in Ciphers | 2 Comments

Bounded gaps: one year on…

Posted on June 1, 2014 by apgoucher

It’s been just over a year since Zhang’s seminal proof that there exist infinitely many pairs of primes separated by a distance at most H = 70000000. There have been many advancements since then, and the current status is a … Continue reading →

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