Pons asinorum

The diagram for Euclid I.5. From Oliver Byrne’s 1847 edition.

The Latin phrase pons asinorum (asses’ bridge) is used for something that is difficult for beginners, but quite simple once you’ve learned it. It’s the nickname of the fifth proposition of Book I of Euclid’s Elements: “In isosceles triangles the angles at the base are equal to one another, and, if the equal straight lines be produced further, the angles under the base will be equal to one another” (Heath, I.251). Euclid’s proof of this proposition is, like skating a backward serpentine, notoriously difficult for beginners. This difficulty and the diagram of the proof (pictured), which looks kind of like a bridge, earned the proposition its nickname by 1780 (Heath, I.415).

The pons asinorum of skating is generally considered the backward serpentine figure (Richardson 1940:34).  Figures are patterns that skaters produce on the ice with their blades. Skating figures requires a lot of concentration. The goal is to get the line on the ice exactly right, then to go over it precisely. The lines left on the ice, called tracings, are the important part. Tiny mistakes in the tracings, invisible to a spectator watching from the sidelines, can determine the outcome of a competition.

The backward serpentine consists of three circles in a row that just touch. The skater starts at the intersection of two of the circles, skates (backwards on one foot) halfway around the middle circle, then, without changing feet, glides all the way around the end circle. Once after reaching the other intersection point, the skater changes feet (“push…with vigor,” advises Maribel Vinson Owen (1962:98)) and completes the remaining 1.5 circles on the other foot.

This figure isn’t very advanced. It has no turns, and the backward change of edge, its main feature, is one of the basic building blocks used in more advanced figures. But it’s quite difficult to learn.

The status of the backward serpentine as the pons asinorum of skating has been challenged. Ernst Jones (1952:154) thinks the backward inside three turn is more deserving of the title because “it gives many skaters a very bad time before they master it.” This is more applicable to today’s skating because skaters struggle with backward inside threes on their moves in the field tests and neglect backward changes of edge.

I also submit the Axel as a candidate for the pons asinorum of skating today. It’s the first jump that many skaters struggle with because of its forward takeoff and the necessary one and a half revolutions in the air.


Sir Thomas Heath. 1956. The Thirteen Books of Euclid’s Elements. New York: Dover.

Maribel Vinson Owen. 1960. The Fun of Figure Skating: A Primer of the Art-Sport.
New York: Harper & Brothers.

T. D. Richardson. 1938. Modern Figure Skating. 2nd ed. London: Methuen & Co.

Ernst Jones. 1952. The Elements of Figure Skating. London: Allen & Unwin.