The Math Of The Mollusk Shell

 

I love finding articles that help support the point of view that math explains the world around us.  I came across on where scientists looked at an extinct mollusk to figure out mathematically how it got its shell shape. The cephalopods include octopus, squid, cuttlefish or nautilus. Historically, the number of extinct species outnumber the current populations with the highest number during the Paleozoic and Mesozoic ages.

Quite a few of the 10,000 species of the extinct cephalopods had tightly coiled shells.  One of those, the Nipponites mirabilis had a shell that twisted so it looked like something M. C. Escher might draw.  The convoluted shell twisted itself so it seemed to have to beginning or ending.

At first, it looks like nothing more than a tangled mass but if you examine it more carefully, you begin to notice there is a pattern to all that twisting.  Several scientists created a mathematical mannequin for this and other shells that did not display the standard pattern.

The mathematical mannequin shows how mechanical forces twist the shell so that it is uneven. In addition, the mannequin also shows how some snails develop their spiraling form.  This mannequin is able to show how three different shells were formed, specifically the spiral shell, the helical shell, and the meandering swerves of the Nipponites mirabilis. In fact, this came out of a desire to understand the physics behind the formation of seashells. 

Mullosks actually create their own shells using the outer mantle which is a fleshy organ.  The mantle actually secrets calcium carbonate in layers that harden into the shell. The scientists designed the mannequin to capture the interactions between the mantle and the outer shell. Although the ancient ammonite the mannequin is based upon died out around 68 million years ago, they had bilateral symmetry similar to their squid cousins. 

The mannequin was to help answer the question of how could a bilateral secretion cause an uneven finished product. One possibility is if the actual body grows faster than the shell, then it can become too big for the shell and cause enough physical stresses to twist the body and cause a twisted shell.  If the conditions are right, it twists unevenly to make the weird shell of the Nippoinits mirabilis. 

This is a cool way to use mathematical modeling. The scientists used currently knowledge and mathematics to create a mathematical model (mannequin) so they could figure out why an ancient mullosk ended up looking like a tangled mess. Let me know what you think, I'd love to hear.  Have a great day.