Monthly Archives: June 2014

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 →

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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 →

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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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