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 History of manifolds and varieties The study of manifolds combines many important areas of mathematics: it generalizes concepts such as curves and surfaces as well as ideas from linear algebra and topology. Certain special classes of manifolds also have additional algebraic structure; they may behave like groups, for instance. In that case, they are called Lie Groups. Alternatively, they may be described by polynomial equations, in which case they are called algebraic varieties, and if they additionally carry a group structure, they are called algebraic groups. The term "manifold" comes from German "Mannigfaltigkeit," by Riemann. In English, "manifold" refers to