The Shape of Shells

Explore the fascinating intersection of mathematics and marine biology in this 52-minute lecture that reveals how simple mathematical principles govern the complex beauty of seashells. Discover the three fundamental stories behind seashell formation through evolution, development, and scientific research, while examining the diverse types including bivalves, gastropods, and ammonites. Learn about the logarithmic spiral that underlies most shell structures and understand the concept of self-similarity in these "eternal" spirals. Investigate how mollusks actually construct their shells through local growth rules involving expansion, rotation, and twist, and uncover why certain shells develop twisting patterns while others remain straight. Examine the formation of spines through growth instability and mismatch, explore the ribbing patterns in ammonites through the tug-of-war model, and understand Buckman's Law relating expansion rates to ribbing. Delve into the mystery of fractal shells with recursive spines and discover how fractal patterns appear throughout nature, from shells to shark teeth. Master the mathematical rules that govern biological fractals and appreciate how humble mollusks create intricate three-dimensional structures following elegant mathematical laws, resolving many enduring questions in biology through mathematical modeling.