What Would the Nautilus Say? Unleashing Creativity in Mathematics!

Too often mathematics is viewed by students and the general public alike as a set of formulas and techniques. However, mathematicians know that it involves so much more than banal procedures and requires deep thought and creativity. In this work we introduce an activity designed to make creative mathematical exploration accessible to young students and still interesting for those with many years of mathematical training. Popular culture often references the nautilus shell as an example of a golden spiral in nature. While many mathematicians assert this claim is false based on the formal definition, others have provided potential avenues for a relationship between the spiral created in the nautilus shell and the golden ratio. We spell out this debate and ask students to explore this question and see what patterns they can find in the nautilus shell. Might an alternative frame give the nautilus shell a golden hue or is it really just fool's gold?