Beryl Beryl Beryl ( ) is a mineral composed of beryllium aluminium cyclosilicate with the chemical formula BeAlSiO. Well-known varieties of beryl include emerald and aquamarine. Naturally occurring, hexagonal crystals of beryl can be up to several meters in size, but terminated crystals are relatively rare. Pure beryl is colorless, but it is frequently tinted by impurities; possible colors are green, blue, yellow, red (the rarest), and white. Beryl is also an ore source of beryllium. The name "beryl" is derived (via , , and ) from Greek βήρυλλος "beryllos" which referred to a "precious blue-green color-of-sea-water stone"; akin to Prakrit
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