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What shape is a pebble?
I've always been intrigued that mathematicians find ways to use numbers in any natural inquiry. The pebble is the latest subject of mathematical exploration...
One question that has been around since the time of Aristotle has now been solved by physicists in France and the US. What shape is a pebble? Douglas Durian of the University of Pennsylvania and colleagues in Strasbourg say that a pebble is "a nearly round object with a near-Gaussian distribution of curvatures".
Pebbles are unlike regular objects such as spheres, which have an equal curvature over the entire surface.
The researchers found that once the corners of their test objects had been eroded away by tumbling them in a pan, the pebble reached a nearly round shape that progressively got smaller in size. Moreover, the final shapes of all the pebbles were similar and therefore only depend on the erosion process itself.
The team calculated the distribution of curvatures around the circumference of each eroded pebble. The plotted distribution indicates that it followed a nearly Gaussian, or bell-shaped, curve.
The researchers have developed a mathematical tool that can "decode" flat pebble shapes and link these to erosion processes -- regardless of the original shape.
Geologists are interested in such processes because it would let them work out if, say, a layer of rock containing that pebble was formed from a lake, a river, an ocean shore or a desert.