The square circle is a perfect oxymoron, which is very useful to riders. This roundabout figure combines circular displacement with straight lines that make up a square. The rider draws a square by running a quarter turn with the waist to turn at each angle and go back to the next angle. When it is executed at the pace, it has the virtue of making the movements of the horse more flexible and smooth. Sometimes, this classic exercise is proposed to prepare the pirouette without specifying the origins. Giambatista Pignatelli, director of the Academy of Naples, was the inventor. This brilliant squire, highly praised by his student Pluvinel, belongs to the new wave of Italian horsemen of the XVIth century. Later, Solomon de La Broue, also a student of Pignatelli, takes up and develops his dressage principles and breaks down each of the established figures. This character is the first to publish a French riding treatise. The name of La Guérinière was always attached to the square circle. In his Cavalry School, he also recommends reversing these circles and proposes variations in which the circle is started with the shoulders and turned while maintaining the inflation. The rider can place the animal’s croup against the wall and the shoulder inwards. Riding, an art of geometry!