Alex's Adventures in Numberland - Alex Bellos [88]
Stockholm’s superelliptical roundabout was copied by other architects, most notably in the design for the Azteca stadium in Mexico City – which held the World Cup final in 1970 and 1986. In fact, Piet Hein’s curve spread to fashion, becoming a feature of 1970s Scandinavian furniture design. It’s still possible to buy superelliptic plates, trays and door-handles from the company run by Piet Hein’s son.
Piet Hein’s playful mind did not stop at the superellipse, however. F his next project, he wondered what a three-dimensional version of the shape would look like. The result was halfway between a sphere and a box. He could have called it a ‘sphox’. Instead, he called it a ‘superegg’.
Supereggstatic: Uri Geller.
One unexpected feature of the superegg was that it could stand on its end without falling. In the 1970s Piet Hein marketed super-eggs made out of stainless steel as a ‘sculpture, novelty or a charm’. They are beautiful, curious objects. I have one on my mantelpiece. Uri Geller also has one. John Lennon gave it to him, explaining that he had received the egg from aliens who visited him in his New York apartment. ‘Keep it,’ Lennon told Geller. ‘It’s too weird for me. If it’s my ticket to another planet, I don’t want to go there.’
CHAPTER SIX
Playtime
Maki Kaji runs a Japanese magazine that specializes in number puzzles. Kaji considers himself an entertainer who uses numbers as the tools of his trade. ‘I feel more like a film or theatre director than a mathematician,’ he explained. I met Kaji at his office in Tokyo. He was neither geeky nor formal, two characteristics one might expect to find in a numbers guy-turned-successful businessman. Kaji was wearing a black T-shirt under a trendy beige cardigan, and a pair of John Lennon glasses. Aged 57, he has a trim white goatee and sideburns, and often grins effervescently. Kaji keenly told me about his other hobbies, besides number puzzles. For instance, he collects rubber bands, and on a recent trip to London found what to him amounted to a glorious cache – a 25g pack of branded rubber bands from WH Smith and a 100g pack from an independent stationer. He also amuses himself by photographing arithmetically gratifying car licence plates. In Japan, licence plates consist of two numbers followed by another two numbers. Kaji carries a small camera at all times and snaps every registration he sees for which the first pair multiplied by each other equals the second pair.
Assuming that no Japanese car has a 00 for the second pair of digits, each plate Kaji photographs is a line in the times tables of the digits 1 to 9. For instance, 11 01 can be thought of as 1×1 = 1. Likewise, 12 02 is 1×2 = 2. We can carry on the list, and work out that there are 81 possible combinations. Kaji has already collected more than 50. Once he has gathered the full set of times tables, he plans to exhibit them in a gallery.
The idea that numbers can entertain is as old as maths itself. The ancient Egyptian Rhind Papyrus, for example, contains the following list as part of the answer to problem 79. Unlike the other problems in the papyrus, this one has no apparent practical application.
Kaji snaps 3 × 5 = 15 in a Tokyo car park.
Houses
7
Cats
49
Mice
343
Spelt
2401*
Hekat†
16,807
Total
19,607
The list is the inventory of seven houses, each of which had seven cats, each of which ate seven mice, each of which ate seven grains of spelt, each of which came from a separate hekat. The numbers form a geometric progression – which is a sequence where each term is calculated by multiplying the previous term by a fixed number, in this case, seven. There are seven times more cats than houses, seven times more mice than cats, seven times more grains of spelt than mice, and seven times more hekats than grains of spelt. We could rewrite the total number of items as 7 + 72 + 73 + 74 + 75.
It wasn’t just