Dr. Loveless Curiosity Lab
Nautilus Growth, Chamber Walls, Fibonacci Comparisons, and 3D Shell Models
A nautilus shell gives a beautiful test case for the idea of constant relative growth. The main curve is a logarithmic spiral, and the chamber walls are built from related spiral pieces that appear as the shell grows.
The first visual loads the saved 2D Desmos JSON directly, compares the fitted nautilus growth rate with the golden spiral, and keeps the original shell colors and chamber-wall construction. The second visual loads the 3D Desmos shell state, so students can watch the rounded shell grow and toggle the top surface on or off.
The four visuals move from a 2D logarithmic-spiral fit to a 3D shell surface, then leave room for parameter experiments and research connections.
This graph can show how changing \(B\), chamber spacing, or wall curvature creates different possible shells.
Use sliders to compare possible shell morphologies.
This graph can compare real shell measurements, Raup-style parameters, or a Fibonacci/golden-spiral construction.
Measurements, citations, and formula comparisons can go here.
This project started with the question of whether a nautilus cross-section could be modeled accurately using only logarithmic spirals and shifted copies of spiral arcs.
The shell image led to a discussion of chamber walls, growth points, and how to reuse points as the shell grows.
From here, students can compare fitted shell parameters, try other shell species, and decide which features require true 3D surfaces rather than 2D curves.
This connects naturally to polar curves, parametric curves, parametric surfaces, curvature, and growth models.