A floating body with no preferred orientation: an experimental realization

TL;DR

This paper experimentally demonstrates a floating body based on Zindler curves that can remain in equilibrium in any orientation, illustrating the interplay of geometry and buoyancy.

Contribution

It introduces a simple physical realization of a shape with neutral equilibrium in any orientation, based on Zindler curves, and explores effects of density variations.

Findings

The floating object remains in neutral equilibrium in any orientation at specific density.

Slight density changes lead to preferred orientations, explained by energy considerations.

The experiment showcases the role of geometry and physical effects like density inhomogeneities.

Abstract

We present a simple experimental realization of a two-dimensional floating body that can remain in equilibrium in any orientation. This system is based on a class of shapes known as Zindler curves, which possess the remarkable geometric property that all chords dividing their area into equal parts have the same length. Using a multilayer fabrication approach, we construct a heart-shaped floating object with an effective density close to one half of that of the surrounding liquid. We show experimentally that, under these conditions, the object exhibits neutral equilibrium with respect to rotation. When the density is slightly varied, preferred orientations emerge, consistent with a simple energy-based description. Our experiments highlight both the accessibility of this classical problem and the subtle role of physical effects such as density inhomogeneities and capillarity. They provide a simple platform to explore the interplay between geometry and buoyancy, and to test geometric results in a tangible setting.