This pattern with kite-shaped tiles can be extended to cover any area, but however big we make it, the pattern never repeats itself. Alison Boyle investigates aperiodic tilings, which have had unexpected applications in describing new crystal structures.
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.
Solitaire is a game played with pegs in a rectangular grid. A peg may jump horizontally or vertically, but not diagonally, over a peg in an adjacent square into a vacant square immediately beyond. The peg which was jumped over is then removed.
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.
'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.
Danielle Stretch looks back at the remarkable life of pioneering mathematician Emmy Amalie Noether (1882-1935). Despite her constant struggles to make her way in a man's world, she made significant contributions to the development of modern algebra.