The Babylonians had a counting system based on the interesting number 60. Not coincidentally, there is that number of seconds in a minute and 60 of the latter in an hour. 60 is the smallest number to have 1, 2, 3, 4, 5 and 6 as its divisors and it is also the smallest number with 12 factors. There are also 60 carbon atoms in a highly innovative synthetic molecule known as buckminsterfullerene. It is shaped like a soccer ball with pentagonal and hexagonal faces. Each of the 60 carbon atoms is a vertex on both a pentagon and a hexagon, but none of the pentagons are adjacent to each other, so there are 60/5 = 12 pentagons. Each pentagon is attached to 5 hexagons but each hexagon is shared by 3 pentagons, so there are 12(5)/3 = 20 hexagons. The structure follows Euler's polyhedron
formula, |V|-|E|+|F| = 2, (where |V|, |E|, |F| indicate the number of
vertices, edges, and faces). If we apply the formula to C 60 – E + (20 + 12) = 2 E = 90, so the molecule has ‘90 edges’. |
Only after it was synthesized (in 1985) was it realized
that C Fullerenes such as C
http://nobelprize.org/nobel_prizes/chemistry/laureates/1996/press.html http://en.wikipedia.org/wiki/Buckminsterfullerene Hugh Aldersey-Williams. |