Surcingle the withers area. It usually has padding to relieve pressure on the horse's spine. A variation of this design is used for equestrian vaulting. Many trainers first teach a young horse to accept girth pressure by strapping on a surcingle before a saddle and girth. The surcingle is commonly used for longeing, often as a base from which to attach training equipment such as side reins, overcheck, lauffer reins (sliding side reins), or chambons. A surcingle is also important in long lining or ground driving, as it provides rings for the long reins to run through. Double longeing, using two
Girth (geometry) width, with the same width "w". All curves of constant width have the same perimeter, the same value "w" as the circumference of a circle with that width (this is Barbier's theorem). Therefore, every surface of constant width is also a surface of constant girth: its girth in all directions is the same number "w". Hermann Minkowski proved, conversely, that every convex surface of constant girth is also a surface of constant width. For a prism or cylinder, its projection in the direction parallel to its axis is the same as its cross section, so in these cases the girth