Gemstone few as one in a million atoms. These so-called impurities are sufficient to absorb certain colors and leave the other colors unaffected. For example, beryl, which is colorless in its pure mineral form, becomes emerald with chromium impurities. If manganese is added instead of chromium, beryl becomes pink morganite. With iron, it becomes aquamarine. Some gemstone treatments make use of the fact that these impurities can be "manipulated", thus changing the color of the gem. Gemstones are often treated to enhance the color or clarity of the stone. Depending on the type and extent of treatment, they can affect the
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