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 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