youcubed: What Would the Nautilus Say? (6-CC)

While the nautilus shell is often represented in popular culture as an example of a golden spiral, according to many mathematicians it is not.

They acknowledge that it is a classic example of a logarithmic spiral, but claim it does not have the growth factor φ (1.618…) required to make it the special case of the logarithmic spiral traditionally deemed the golden spiral. We ask, could an alternative frame or change in axioms give the nautilus shell a golden hue? What other patterns might be hiding in its shell?

We offer two different task pages so you can choose what is appropriate for your students. We are excited for students to seek patterns by measuring and analyzing ratios.


Algebra & Pre-Algebra, Logarithms, Patterning & Sequencing
Middle School, High School, College, Educator

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youcubed (Stanford University)

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Download lesson plan.