That's Maths

The term ‘Chaos Game’ was coined by Michael Barnsley, who developed this ingenious technique for generating mathematical objects called fractals. The Chaos Game is a simple algorithm that identifies one point in the plane at each stage. The sets of points that ultimately emerge from the procedure are remarkable for their intricate structure. The relationship between the algorithm and fractal sets is not at all obvious because there is no evident connection between them. This element of surprise is one of the delights of mathematics.

A link to a page is regarded as an indicator of popularity and importance, with the value of this link increasing with the popularity of the page linking to it. The key idea is that a web page is important if other important pages link to it.
Thus, PageRank is a popularity contest: it assigns a score to each page according to the number of links to that page and the score of each page linking to it. So it is recursive: the PageRank score depends on PageRank scores of other pages, so it must be calculated by an iterative process, cycling repeatedly through all the pages. At the beginning, all pages are given equal scores. After a few cycles, the scores converge rapidly to fixed values, which are the final PageRank values.

showing this is possible: the formula for a great circle turns out to be one of Napier’s Rules

rossing a road, you observe oncoming traffic, estimate its speed and time to arrive, reckon the time needed to cross, compare the two and decide whether to walk or to wait.

A man weighing 100 kg can lose about half a kilo by moving from Anchorage to Zanzibar but, of course, his body mass does not change, only the pull of the earth upon it

rely critically on secure communications, using encryption methods that spring directly from number theory

If you have a general interest in scientific matters and wish to be inspired by the beauty and power of mathematics, this book should serve you well

no longer attract active professional research but that still hold fascination

articles. Beauty can be subjective, but, as you learn more, you cannot fail to be impressed by the majesty and splendour of the intellectual creations of some of the world’s most brilliant minds

The byline of my blog, thatsmaths.com, is ‘Beautiful, Useful and Fun