<p>On the door of his Academy, Plato wrote, “Those who do not know geometry cannot enter,” because politics and democracy are concepts of equilibrium in the geometric sense. The core concern in a democracy is the geometrical balance between the opposing concepts of governor-governed, equality-freedom, and individual-society-state. If the geometrical equilibrium of democracy is out-of-balance, for example, the governor is prioritized over the governed, equality is prioritized over freedom, or the individual-society-state balance is disrupted, the result is either anarchy or tyranny. Many philosophers who have pondered politics have focused on the concepts of “balance” and “the balance of democracy.” However, in these works, the idea of balance is not analyzed and remains abstract. In this comparison of Turkish and American democracies, the geometric balance of democracy is concretized by placing the concepts of individual, society, and state at the corners of an equilateral triangle that embodies the geometric balance of democracy. An examination of the triangle’s interior angles supports the argument that American democracy is in a more balanced position than Turkish democracy.</p>