Hermit crab on physical characteristics, genetic information, and combined data, support the longstanding hypothesis that the king crabs in the family Lithodidae are derived hermit crabs and should be classified as a family within Paguroidea. Other researchers have challenged this, asserting that the Lithodidae (king crabs) should be placed with the Hapalogastridae in a separate superfamily Lithodoidea. Six families are formally recognized in the superfamily Paguroidea, containing around 1100 species in total in 120 genera. The fossil record of "in situ" hermit crabs using gastropod shells stretches back to the Late Cretaceous. Before that time, at least some hermit crabs used ammonites'
History of manifolds and varieties spaces with a differentiable or topological structure, while "variety" refers to spaces with an algebraic structure, as in algebraic varieties. In Romance languages, manifold is translated as "variety" – such spaces with a differentiable structure are literally translated as "analytic varieties", while spaces with an algebraic structure are called "algebraic varieties". Thus for example, the french word "" means topological manifold. In the same vein, the Japanese word "" (tayōtai) also encompasses both manifold and variety. ("" (tayō) means various.) Ancestral to the modern concept of a manifold were several important results of 18th and 19th century mathematics. The oldest