This geological fascination led to Palais’s most provocative unpublished manuscript, La Corne Infinie (The Infinite Horn). In it, he posed a question that married differential geometry with set theory: Can a two-dimensional surface of constant negative curvature (a hyperbolic plane) be embedded in three-dimensional Euclidean space in such a way that it forms a single, unbounded “horn” of finite volume but infinite surface area? The Big Horn, he argued, was nature’s imperfect suggestion of such an object — a crumpled sheet of rock that infinitely recedes into detail. Mathematically, this would be a counterexample to the idea that volume bounds area. While known surfaces like the “pseudosphere” achieve this property for a horn of revolution, Palais wanted a wild embedding, one that twisted back on itself like the faulted strata of the Bighorn anticline.
For most people, "Big Horn" might evoke the rugged mountain range spanning the border of Wyoming and Montana, the battlefield where Custer made his last stand, or perhaps the wild sheep that roam those rocky peaks. For a dedicated legion of motorcycle enthusiasts and collectors, however, "Big Horn" is associated with something entirely different: a piece of American two-wheeled history. In France, this passion has found a fervent ambassador in Jacques Palais, a collector whose devotion to the iconic Big Horn model has made him a notable figure in the world of vintage motorcycle preservation. jacques palais big horn
The 1870s uniforms—featuring high leather boots, bright brass buttons, and distinctive hats—are a major focal point in the series. The films frequently feature close-ups of the cavalry gear to underscore the soldiers' pride before their tragic defeat. 2. Hand-to-Hand and Close Quarters Combat Mathematically, this would be a counterexample to the