Hermit crab gives rise to the popular name "hermit crab", by analogy to a hermit who lives alone. Several hermit crab species, both terrestrial and marine, have been observed forming a vacancy chain to exchange shells. When an individual crab finds a new empty shell it will leave its own shell and inspect the vacant shell for size. If the shell is found to be too large, the crab goes back to its own shell and then waits by the vacant shell for up to 8 hours. As new crabs arrive they also inspect the shell and, if it is too big,
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