The Mathematical Study of Mollusk Shells

3. Nautilus and the Ammonites

Not many shells exhibit the logarithmic spiral in its simplest, planar form. The main living example is the cephalopod Nautilus pompilius. There are many examples (all extinct) in the cephalopod subclass Ammonoidea.

Shell of Nautilus pompilius sliced acrossto show inner chambers. Image from Sanibel Seashell Industries, used with permission.	A mathematical model of Nautilus.Model details.
Fossil of the Ammonite Astroceras obtusum.Image from Paleopalace.com,used with permission. This specimen, measuring approx. 4 inchesin diameter, is from the lower Lias formation in Dorset, England.It is about 200 million years old.	A mathematical model of Astroceras. Model details.
Fossil Ammonite Euhoplites truncatus.Image @2000 Jim Craig from Fossils of the GaultClay and Folkestone Beds of Kent, UK, used with permission.	A mathematical model of Euhoplites. Model details.
Fossil Bellerophina minuta. Long thought tobe a cephalopod, recently reclassified in the Gastropoda.Image @2000 Jim Craig from Fossils of the GaultClay and Folkestone Beds of Kent, UK, used with permission.	A mathematical model of Bellerophina. Model details.

• 1. Terminal growth and unchanging form

• 2. Zoning laws in Molluskville

• 3. Nautilus and the Ammonites

• 4. Things get more complicated in 3 dimensions, but Calculus comes to the rescue.

• 5. Mathematical models of helical shells

• 6. Ray Gildner's Java applet for shell sketching

• 7. For further thought