Horseshoe to the modern hoof boot. Historians differ on the origin of the horseshoe. Because iron was a valuable commodity, and any worn out items were generally reforged and reused, it is difficult to locate clear archaeological evidence. Although some credit the Druids, there is no hard evidence to support this claim. In 1897 four bronze horseshoes with what are apparently nail holes were found in an Etruscan tomb dated around 400 B.C. The assertion by some historians that the Romans invented the "mule shoes" sometime after 100 BC is supported by a reference by Catullus who died in 54 BC.
Horseshoe map class of horseshoe maps simple, the curved region of the horseshoe should not map back into the square. The horseshoe map is one-to-one, which means that an inverse "f" exists when restricted to the image of under . By folding the contracted and stretched square in different ways, other types of horseshoe maps are possible. To ensure that the map remains one-to-one, the contracted square must not overlap itself. When the action on the square is extended to a diffeomorphism, the extension cannot always be done in the plane. For example, the map on the right needs to be extended