This geometric incompatibility gives roses their unique shape 🌹

Researchers at the Hebrew University of Jerusalem combined theory, modeling, and experimentation to understand the growth of rose petals. Their work, published in Science, reveals the influence of a geometric incompatibility on the flower's final morphology.


The incompatibility, called Mainardi-Codazzi-Peterson, prevents petals from following their natural curvature, creating sharp edges and cusps. This phenomenon contrasts with that observed in most other flowers, which are subject to Gauss incompatibility.

The Mainardi-Codazzi-Peterson incompatibility describes a situation where the geometric conditions necessary for surface coherence are violated. In the case of rose petals, this prevents uniform curvature, leading to the formation of unusual structures.

It differs from Gauss incompatibility, more common in nature, which produces wavy patterns without sharp edges.


Numerical simulations and flexible plastic discs helped validate the scientists' hypotheses. They highlight the unique nature of roses in the plant kingdom, with potential implications for shape-changing controlled materials.