A microbe with flagella rows through water the way a person rows with their arms. But if a person swims breaststroke, they go forward, while a microbe goes in a spiral. The reason is that a microbe has no single direction: each part of its surface pushes water in its own direction, and the body twists like a corkscrew.

The authors of the study took a swimmer of any shape, resembling a sphere, and decomposed its surface sliding into simple components, like breaking music into notes. It turned out that if the melody doesn't change, the swimmer always traces a helical path in space. For an elongated swimmer, resembling a rice grain, they derived exact formulas linking shape and stroke style to translational and rotational speeds.

Then they asked: how should one paddle to expend the least energy? First, they fixed the direction of motion and found the most economical stroke. Then they allowed the swimmer to choose its own direction. It turned out that the choice between "swimming straight" and "spinning in place" depends on the symmetry of the body. Symmetric shapes prefer straight paths, while slightly skewed ones prefer circling.

This approach helps us understand how natural microswimmers are built and how to design artificial ones that move without wasting energy.