Alex's Adventures in Numberland (Alex Bellos)

A relatively lightweight dip into a number of aspects of mathematics and how they impact on our lives today.  You don't need to remember much school maths to enjoy the book (but you do need an interest in it).  Full of interesting facts and quirks - the best has to be a drill bit that drills square holes!



Locn. 469-70 the study found a strong correlation between a talent at reckoning and success in formal maths. The better one’s approximate number sense, it seems, the higher one’s chance of getting good grades.
Locn. 1496-1500 The Menger sponge is a brilliantly paradoxical object. As you continue the iterations of taking out smaller and smaller cubes the volume of the sponge gets smaller and smaller, eventually becoming invisible – as though the woodworm have eaten the whole lot. Yet each iteration of cube removal also makes the surface area of the sponge increase. By taking more and more iterations you can make the surface area larger than any area you want, meaning that as the number of iterations approaches infinity, the surface area of the sponge also approaches infinity.
Locn. 2633 Pi exhibits randomness non-randomly – which is fascinating, and weird.
Locn. 2686-88 One useful property of a Reuleaux triangle is that it can be rotated inside a square so that it touches all four sides of the square at all times. This property was exploited by Harry James Watts, an English engineer living in Pennsylvania, in 1914, when he designed one of the most bizarre tools in existence: a drill that can drill square holes.
Locn. 4560-63 The mathematical reason why the golden angle produces the best leaf arrangement around a stem is linked to the concept of irrational numbers, which are those numbers that cannot be expressed as fractions. If an angle is an irrational number, no matter how many times you turn it around a circle you will never get back to where you started. It may sound Orwellian, but some irrational numbers are more irrational than others. And no number is more irrational than the golden ratio.
Locn. 5480-82 Adolphe Quételet has good claim to being the world’s most influential Belgian. (The fact that this is not a competitive field in no way diminishes his achievements.) Locn. 5495 In Brussels in 1853 Quételet hosted the first international conference on statistics.
Locn. 5557 the quincunx. The word’s original meaning is the pattern of five dots on a die,