The seemingly magical ability of a spinning top to stay upright fascinated people for many thousands of years and in many civilizations. Clay spinning tops dated to about 6,000 years ago were excavated in Iraq. And for all these millenia another similarly counterintuitive phenomenon hovered undiscovered until 1908, when Stephenson observed that imposing periodic oscillation on the pivot of a pendulum can stabilize the upside-down equilibrium. Later other similarly counterintuitive effects were discovered – and some used in physical experiments. Traditionally this physically appealing subject has been treated by formal computation - an effective practical tool which, however, does not explain what is really going on. By contrast, a geometrical approach can reveal the reasons for the mysterious behavior - although some open questions still remain.
Mark Levi is a Professor of Mathematics at Penn State. You can learn more about Mark Levi on his website.