Four-dimensional spaceFour-dimensional space (4D) is the mathematical extension of the concept of three-dimensional space (3D). Three-dimensional space is the simplest possible abstraction of the observation that one needs only three numbers, called dimensions, to describe the sizes or locations of objects in the everyday world. For example, the volume of a rectangular box is found by measuring and multiplying its length, width, and height (often labeled x, y, and z).
MuscoviteMuscovite (also known as common mica, isinglass, or potash mica) is a hydrated phyllosilicate mineral of aluminium and potassium with formula KAl2(AlSi3O10)(F,OH)2, or (KF)2(Al2O3)3(SiO2)6(H2O). It has a highly perfect basal cleavage yielding remarkably thin laminae (sheets) which are often highly elastic. Sheets of muscovite 5 meters × 3 meters (16.5 feet × 10 feet) have been found in Nellore, India. Muscovite has a Mohs hardness of 2–2.25 parallel to the [001] face, 4 perpendicular to the [001] and a specific gravity of 2.
AmphiboleAmphibole (ˈæmfəboʊl) is a group of inosilicate minerals, forming prism or needlelike crystals, composed of double chain SiO4 tetrahedra, linked at the vertices and generally containing ions of iron and/or magnesium in their structures. Its IMA symbol is Amp. Amphiboles can be green, black, colorless, white, yellow, blue, or brown. The International Mineralogical Association currently classifies amphiboles as a mineral supergroup, within which are two groups and several subgroups.
BiotiteBiotite is a common group of phyllosilicate minerals within the mica group, with the approximate chemical formula . It is primarily a solid-solution series between the iron-endmember annite, and the magnesium-endmember phlogopite; more aluminous end-members include siderophyllite and eastonite. Biotite was regarded as a mineral species by the International Mineralogical Association until 1998, when its status was changed to a mineral group. The term biotite is still used to describe unanalysed dark micas in the field.
Character (mathematics)In mathematics, a character is (most commonly) a special kind of function from a group to a field (such as the complex numbers). There are at least two distinct, but overlapping meanings. Other uses of the word "character" are almost always qualified. multiplicative character A multiplicative character (or linear character, or simply character) on a group G is a group homomorphism from G to the multiplicative group of a field , usually the field of complex numbers.
