Google Classroom
GeoGebraGeoGebra Classroom

Gnomonic Growth of the Nautilus

“The image below is a cross section of the chambered nautilus. The chambered nautilus builds its shell in stages, each time adding another chamber to the already existing shell. At every stage of its growth, the shape of the chambered nautilus shell remains the same–the beautiful and distinctive spiral. This is a classic example of gnomonic growth–each new chamber added to the shell is a gnomon of the entire shell. The gnomonic growth of the shell proceeds, in essence, as follows: Starting with its initial shell (a tiny spiral similar in all respects to the adult spiral shape), the animal builds a chamber (by producing a special secretion around its body that calcifies and hardens). The resulting, slightly enlarged spiral shell is similar to the original one. Each new chamber adds a gnomon to the shell, so the shell grows and yet remains similar to itself.” From Excursions In Modern Mathematics, by Tannenbaum