* Sprouts* is a simple and delightfully subtle pencil-and-paper game for two players. The game is set up by marking a number of spots on a page. Each player makes a move by drawing a curve that joins two spots, or that loops from a spot back to itself, without crossing any lines drawn earlier, and then marking a new spot on the curve. Continue reading ‘Sproutology’

## Archive for August, 2012

### Analemmatic Sundials

Published August 16, 2012 Irish Times ClosedTags: Spherical Trigonometry, Time measurement

**This week’s That’s Maths article, TM003, describes the analemmatic sundial on the East Pier in Dun Laoghaire.
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**An article in Plus Magazine, by Chris Sangwin and Chris Budd, gives a description of the theory of these sundials and instructions on how to build one.**

**A script to design an analemmatic sundial, written by Alexander R. Pruss, is available here. To run it, just enter the width of the sundial, the latitude and longitude, and the timezone. The script will generate all the required dimensions.**

**Here is a technical article, The Equation of Time and the Analemma (PDF), submitted to the Bulletin of the Irish Mathematical Society.**

Spherical trigonometry is not in vogue. A century ago, a Tripos student might resolve a half-dozen spherical triangles before breakfast. Today, even the basics of the subject are unknown to many students of mathematics. That is a pity, because there are many elegant and surprising results in spherical trigonometry. For example, two spherical triangles that are similar – having corresponding angles equal – have the same area. This contrasts sharply with the situation for plane geometry. Continue reading ‘Napier’s Nifty Rules’

**This week’s That’s Maths article, at TM002, describes how Google’s PageRank software finds all those links when you enter a search word, by solving an enormous problem in linear algebra.**

**A comprehensive description of PageRank is given in the book Google’s PageRank and Beyond: The Science of Search Engine Rankings, by Amy N. Langville & Carl D. Meyer This book won an AAP Award in 2006 for Best Professional/Scholarly Book in Computer & Information Science.**