Fuji (apple) list of most popular apples, only trailing Red Delicious and Gala. Fuji apples are grown in traditional apple-growing states such as Washington, Michigan, New York, and California. Washington State, where more than half of America's apple crop is grown, produces about 135,000 tons of Fuji apples each year, third in volume behind Red Delicious and Gala varieties. Fuji apples have recently been projected by the US Apple Association to be in 4th place as America's favorite apple. Many sports (mutant cultivars) of the Fuji apple have been recognized and propagated. In addition to those that have remained unpatented, twenty had
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