The Math of Beach Pebble Formation

Modeling how abrasion shapes objects has challenged scientists for centuries, from Aristotle to planetary geologists studying Mars.

Mathematics Physics Geology

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May-June 2023

Volume 111, Number 3
Page 168

DOI: 10.1511/2023.111.3.168

More than 2,300 years ago, Aristotle pondered the shapes of beach stones and proposed that the abrasion of a pebble is more rapid at locations farther from its center, because those regions can receive greater abrasive impulses. He concluded that beach stones evolve toward spheres. But the pebbles used in designs from Stone Age ceremonies (see images below) to modern art are not spherical at all. Rather, they have the familiar oval shape of the stones on a beach on Banks Peninsula in New Zealand, shown in the next section.

Courtesy of J. Perrot; © The Israel Museum, Jerusalem

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