Modeling A Chicken Egg Math Ia Apr 2026

~600-700 words I’m deep into IA season, and I wanted to share a topic that’s been equal parts frustrating and fascinating: modeling the shape of a chicken egg.

[ SA = 2\pi \int_{-L/2}^{L/2} f(x) \sqrt{1 + [f'(x)]^2} dx ] modeling a chicken egg math ia

Good luck with your IAs! 🥚📐

This equation worked beautifully for the top half. The bottom half is symmetric (y negative). Once I had ( y = f(x) ) for the upper half (from ( x = -L/2 ) to ( x = +L/2 )), I used: ~600-700 words I’m deep into IA season, and

Why an egg? At first, it sounds simple. But an egg isn’t a sphere, an ellipsoid, or an oval—it’s a unique mathematical object with one blunt end, one pointed end, and a perfect curve. And since I love calculus and real-world applications, this felt like a goldmine. My research question is: How can we model the 2D profile of a chicken egg using a combination of functions, and then use calculus to find its volume and surface area? The goal: create a mathematical model that fits an actual egg’s silhouette, then compare theoretical vs. measured volume (using water displacement). Step 2 – Gathering Data I took a standard large chicken egg, traced its outline on grid paper, and digitized key coordinates. Then came the hard part: finding an equation that fits. The bottom half is symmetric (y negative)

[ y = \pm \frac{B}{2} \sqrt{\frac{L^{2} - 4x^{2}}{L^{2} + 8wx + 4w^{2}}} ]