The question of whether objects other than spheres can float in equilibrium in all orientations, known as Ulam's floating body problem, has long intrigued mathematicians. Research has confirmed the existence of such shapes, including Zindler curves in two dimensions and similar bodies in three dimensions.
It was within this context that Lucie Pontiggia, a student at ESPCI, took on the challenge during a research internship at the Institut Langevin in the summer of 2025. Guided by doctoral student Angélique Campaniello, she designed and built a heart-shaped floater based on a Zindler curve. An experiment was then set up to study its behavior.
The results are conclusive: when its density is close to half that of the liquid, the heart indeed floats in equilibrium, regardless of its orientation. This marks the first experimental realization of this property. The experiment also highlighted the influence of non-ideal physical phenomena, such as surface tension.
This work, completed just months after Lucie Pontiggia's internship, led to a publication in the American Journal of Physics and graced its cover. The article is co-authored by Lucie Pontiggia, Angélique Campaniello, and Emmanuel Fort.
Beyond the scientific achievement, this experiment perfectly illustrates the importance of research-based training at ESPCI. From the first year, students are exposed to research, particularly through short internships supported by Université PSL as part of the UROP program. Team-based scientific projects, conducted over a year, allow students to explore original questions and achieve top-tier scientific publications, and even patent filings.
This floating heart thus testifies to the value of research-based education from the very beginning of the university curriculum.
