'Of the myriad strategems I employ to avoid useful work, the one I most enjoy is to envision how scientists of earlier eras would have made use of modern computers.' John L. Casti tells us how today's mathematicians are using computers to carry on the work of turn-of-the-century polymath d'Arcy Wentworth Thompson, who showed how mathematical functions could be applied to the shape of one organism to continuously transform it into other, physically similar organisms.
The harmonic series is far less widely known than the arithmetic and geometric series. However, it is linked to a good deal of fascinating mathematics, some challenging Olympiad problems, several surprising applications, and even a famous unsolved problem. John Webb applies some divergent thinking, taking in the weather, traffic flow and card shuffling along the way.
Actuarial science began as the place where two branches of mathematics meet: compound interest and observed mortality statistics. Financial planning for the future is therefore rooted firmly in the past. John Webb takes us through some of the mathematics involved, introducing us to some of the colourful characters who led the way.
One of the most striking and powerful means of presenting numbers is completely ignored in the mathematics that is taught in schools, and it rarely makes an appearance in university courses. Yet the continued fraction is one of the most revealing representations of many numbers, sometimes containing extraordinary patterns and symmetries. John D. Barrow explains.

The German mathematician Adam Ries (1492-1559) was the author of the most successful textbook of commercial arithmetic of his day. The book, published in 1552, earned such a high reputation that the German phrase nach Adam Ries is used to this day to indicate a correct calculation.

We've all seen a traditional sundial, where a triangular wedge is used to cast a shadow onto a marked-out dial - but did you know that there is another kind? In this article, Chris Sangwin and Chris Budd tell us about a different kind of sundial, the analemmatic design, where you can use your own shadow to tell the time.