Hermit crab increased prevalence of marine debris, but also due to depletion of seashells from beaches due to humans collecting them. Hermit crab species range in size and shape, from species with a carapace only a few millimetres long to "Coenobita brevimanus", which can live 12–70 years and can approach the size of a coconut. The shell-less hermit crab "Birgus latro" (coconut crab) is the world's largest terrestrial invertebrate. The young develop in stages, with the first two (the nauplius and protozoea) occurring inside the egg. Most hermit crab larvae hatch at the third stage, the zoea. In this larval stage, the
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