Mathematical Modeling of the Nautilus Shell

Abstract

UniverCity is a now biennial event that Ball State University and the City of Muncie sponsor to benefit the community. This year’s theme was Celebrate Community and the symbol was the nautilus shell. UniverCity provided this statement: “The magnificent Nautilus Shell was chosen as a symbol for the UniverCity 2002 festival at Ball State University. With the theme Celebrate Community, UniverCity 2002 was focused upon cooperation, collaboration and connections among and between people. The Nautilus Shell found a strong fit with our theme. This shell, like a community, gains its strength through the harmonious coming together of its many individual parts. It grows outward from a strong center, like our towns and cities. Its spiral geometry evokes order and proportion. Its rainbow of color reflects the diversity and richness so essential to a healthy, vibrant community. Lastly, the simple outer appearance of the Nautilus belies its phenomenal inner beauty—symbolic of the inner beauty and magic so inherent to people and communities.” Departments were invited to do a project to share with the community. The Department of Mathematical Sciences chose to do a mathematical modeling of the shape of the nautilus shell. Our team consisted of Josh Drew and me, and our faculty advisor was Dr. Giray ¨Okten. We used the following polar equation to model the spiral shape of the shell: