Gemstone beryl. Gemstone pricing and value are governed by factors and characteristics on the quality of the stone. These characteristics include clarity, rarity, freedom of defects, beauty of the stone, as well as the demand for them. There are different pricing influencers for both colored gemstones, and for diamonds. The pricing on colored stones is determined by market supply-and-demand, but diamonds are more intricate. Diamond value can change based on location, time, and on the evaluations of diamond vendors. There are a number of laboratories which grade and provide reports on gemstones. Each laboratory has its own methodology to evaluate gemstones.
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