Hermit crab crab has several long spines, a long, narrow abdomen, and large fringed antennae. Several zoeal moults are followed by the final larval stage, the megalopa. Hermit crabs are often seen as a "throwaway pet" that would live only a few months, but species such as "Coenobita clypeatus" have a 23-year lifespan if properly treated, and some have lived longer than 32 years. Hermit crabs are more closely related to squat lobsters and porcelain crabs than they are to true crabs (Brachyura). However, the relationship of king crabs to the rest of Paguroidea is a highly contentious topic. Many studies based
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