Mathematical Modelling of Egg Geometry to Determine Shape Index, Surface Area, and Volume

This investigation explores the mathematical modelling of an egg's asymmetric geometry to determine its Egg Shape Index (SI), surface area, and volume. The author modifies the standard ellipse equation by introducing a linear parameter to account for varying curvature, solving for constants using coordinate intercepts.

Calculus is applied through solids of revolution, utilizing the chain rule, quotient rule, and u-substitution for integration. The study concludes the egg is "standard" (SI ≈ 72.4) with a volume of 53.3 cm³. The exemplar is particularly valuable for its comparative validation against the Nobuo Yamamoto model, demonstrating high precision with negligible percentage errors.