Can you imagine objects that you can't measure? Not ones that don't exist, but real things that have no length or area or volume? It might sound weird, but they're out there. Andrew Davies gives us an introduction to Measure Theory.
During World Mathematical Year 2000 a sequence of posters were displayed month by month in the trains of the London Underground aiming to stimulate, fascinate - even infuriate passengers! Keith Moffatt tells us about three of the posters from the series.
It's worth pointing out right at the start that this wouldn't be a particularly good choice of calendar if you actually want to keep track of the year. The calendar is large (A2 size) but the days of the month occupy only a 1cm-high section of each page - and the day names aren't even included, just their numbers.
The golden section (or golden ratio), famously, was used in antiquity, when the ancient Greeks built temples the proportions of whose parts - by accident or design - are often supposed to have fallen in the golden ratio.
The author says in the introduction that "this book is intended as a polemic", and a polemic it certainly is. Whether or not you like the book will therefore depend not only on whether you agree with his thesis, but also on whether or not you like polemic.
The paradoxes of the philosopher Zeno, born approximately 490 BC in southern Italy, have puzzled mathematicians, scientists and philosophers for millennia. Although none of his work survives today, over 40 paradoxes are attributed to him which appeared in a book he wrote as a defense of the philosophies of his teacher Parmenides.