Your World: Iconic Geometry
BBC World Service

The first in a short series of programmes (27 August, 2.05pm) about the significance of various geometric shapes considered "a story of
infinity, symmetry and efficiency as profound to humanity as it is useful to Mother Nature. One of the oldest figures in mathematics -
the shape of circle!"

What followed was an episode crammed with biologists from Imperial College, algebra professors and astrophysicists from the super-Ballardian-sounding Centre for Cold Matter, devoted to the study of fundamental problems in physics using atomic lasers. On these stellar presences came, unfurling themselves from the car, so to speak, and distractedly shaking the hand of the presenter, Cecil Balmond (no slouch, being director of the oblong-spectacled Non-Linear Systems Organisation, a material and structural research unit), before turning to run their forefingers over the data.

Stonehenge, we were informed, was "designed on some prehistoric drawing board". "Uh, huh," nods Balmond. "Somehow." "Uh, huh." How did they manage to position accurately such massive lumps of rock so that, on the solstice, the rising sun cuts directly through the centre? The answer, which, as we all know, has for 5,000 years been "Search me" - the equivalent of a square-nosed vehicle soothingly edging its way on to a muddy track - suddenly came on as sharp as scissors.

“See this hexagon that's drawn within the circle?" "Absolutely." "Well, they drew a pentagon and let one of the vertices of the pentagon share one of the vertices of the hexagon." "OK." "They could do sizes. They could do tens. They could do squares. And they could do a 30-sided triacontagon. These are celestial markers, tracing circles through space in our galaxy and beyond!"

Balmond, always so politely inquisitive, a perfect male wedding guest, one always feels (he's equally capable of discussing caesareans and intra-coastal waterways), now did what was patently required and threw himself entirely at the mercy of the adverb. "Interesting how they hollowed it out to fit on the protrusion from the vertical." "Absolutely." "It's an abstraction of the human facility, even then." "Absolutely." "The night sky is partly a sphere. The horizon is a circle that surrounds." "Absolutely." "What speed should I travel down this electron beam?" "Huh?"