A mathematical exposition of balance in the perception of avian egg shape and its relationship to human notions of “harmonic” structures – from symmetry to asymmetry

Eggs are regarded to be harmonious and aesthetic structures, with their shape used in art, architecture, design and engineering applications. Considering that they combine many different shapes, from symmetrical (ellipsoid) to asymmetrical (though bilaterally symmetrical), we herein aimed to develop mathematical principles that allow us to formalize a definition of the degree of harmony in egg-shaped figures. Proposing a “principle of balance”, in which the basis of the most aesthetic shape demonstrated equality of volumes/projection areas in pointed and blunt ends, we developed computational dependences, with which one can select the parameters of eggs so that their shape meets these principles. We demonstrate that two famous artworks do not adhere to such principles but describe how it could, theoretically, be possible to alter the egg shapes in them so that their aesthetic perception may be reconsidered. We generated, by artificial intelligence, an egg shape defined on the condition that it most represents the most aesthetic shape to the human eye, finding that it fully complied with our balance principles. Since “harmony” is a subjective term and individual perceptions of it may vary, we consider the appropriateness of formalization in determining the degree of aesthetics of egg shape, while adhering to the general perception of a bird’s egg due to its asymmetric geometric structure. Aspects of our findings may have practical applications in agriculture, architecture, design and/or engineering.