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 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