
Monday, August 10, 1998 Published at 18:03 GMT 19:03 UK Sci/Tech Staggering solution to sphere stacking Greengrocers have been getting it right for centuries
Thomas Hales posted his solution to Kepler's stacking problem on the Internet on Sunday. Professor Hales has proved what no scientist has been able to for 300 years  in a solution which has been practiced by greengrocers through the centuries.
Harriot subsequently wrote to German astronomer Johannes Kepler, who discovered the laws that describe the orbits of the planets. In 1611, Kepler suggested the most efficient way to pack spheres in the smallest space was an arrangement known as facecentred cubic packing, which is how greengrocers stack their oranges. The bottom layer is arranged in lines which are alternately staggered by half an orange. The stack is built up by placing the oranges in the dimples of the layer below. Kepler could never prove there was a more efficient way and ever since generations of mathematicians have since been trying to find conclusive proof about whether he was correct.
It contains 250 pages of logic and relies on computer programs which require more than three gigabytes of storage space.
Now Professor Hales is taking a break from the research which has taken him several years to complete along with research student Samuel P Ferguson. Dr Simon Singh said the problem is one every mathematician would have liked to have solved. He said: "There's an infinite number of arrangements. "The question is how you can ever prove there isn't some other arrangement you haven't encountered.
"That's what people have been doing for the last 400 years  trying to find out whether or not there is a better arrangement than Kepler's suggestion." 
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