Hyperbolic geometryIn mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with: For any given line R and point P not on R, in the plane containing both line R and point P there are at least two distinct lines through P that do not intersect R. (Compare the above with Playfair's axiom, the modern version of Euclid's parallel postulate.) The hyperbolic plane is a plane where every point is a saddle point.
Projective geometryIn mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared to elementary Euclidean geometry, projective geometry has a different setting, projective space, and a selective set of basic geometric concepts. The basic intuitions are that projective space has more points than Euclidean space, for a given dimension, and that geometric transformations are permitted that transform the extra points (called "points at infinity") to Euclidean points, and vice-versa.
Synthetic geometrySynthetic geometry (sometimes referred to as axiomatic geometry or even pure geometry) is geometry without the use of coordinates. It relies on the axiomatic method for proving all results from a few basic properties initially called postulate, and at present called axioms. The term "synthetic geometry" has been coined only after the 17th century, and the introduction by René Descartes of the coordinate method, which was called analytic geometry.
Cyclic compoundA cyclic compound (or ring compound) is a term for a compound in the field of chemistry in which one or more series of atoms in the compound is connected to form a ring. Rings may vary in size from three to many atoms, and include examples where all the atoms are carbon (i.e., are carbocycles), none of the atoms are carbon (inorganic cyclic compounds), or where both carbon and non-carbon atoms are present (heterocyclic compounds with rings containing both carbon and non-carbon).
Equatorial coordinate systemThe equatorial coordinate system is a celestial coordinate system widely used to specify the positions of celestial objects. It may be implemented in spherical or rectangular coordinates, both defined by an origin at the centre of Earth, a fundamental plane consisting of the projection of Earth's equator onto the celestial sphere (forming the celestial equator), a primary direction towards the vernal equinox, and a right-handed convention.
AtomAn atom is a particle that consists of a nucleus of protons and neutrons surrounded by a cloud of electrons. The atom is the basic particle of the chemical elements, and the chemical elements are distinguished from each other by the number of protons that are in their atoms. For example, any atom that contains 11 protons is sodium, and any atom that contains 29 protons is copper. The number of neutrons defines the isotope of the element. Atoms are extremely small, typically around 100 picometers across.
Celestial equatorThe celestial equator is the great circle of the imaginary celestial sphere on the same plane as the equator of Earth. By extension, it is also a plane of reference in the equatorial coordinate system. In other words, the celestial equator is an abstract projection of the terrestrial equator into outer space. Due to Earth's axial tilt, the celestial equator is currently inclined by about 23.44° with respect to the ecliptic (the plane of Earth's orbit), but has varied from about 22.0° to 24.
Algebraic geometryAlgebraic geometry is a branch of mathematics which classically studies zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros. The fundamental objects of study in algebraic geometry are algebraic varieties, which are geometric manifestations of solutions of systems of polynomial equations.
AmineIn chemistry, amines (əˈmi:n,_ˈæmi:n, ˈeɪmiːn) are compounds and functional groups that contain a basic nitrogen atom with a lone pair. Amines are formally derivatives of ammonia (), wherein one or more hydrogen atoms have been replaced by a substituent such as an alkyl or aryl group (these may respectively be called alkylamines and arylamines; amines in which both types of substituent are attached to one nitrogen atom may be called alkylarylamines). Important amines include amino acids, biogenic amines, trimethylamine, and aniline.
Equatorial mountAn equatorial mount is a mount for instruments that compensates for Earth's rotation by having one rotational axis, called polar axis, parallel to the Earth's axis of rotation. This type of mount is used for astronomical telescopes and cameras. The advantage of an equatorial mount lies in its ability to allow the instrument attached to it to stay fixed on any celestial object with diurnal motion by driving one axis at a constant speed. Such an arrangement is called a sidereal drive or clock drive.
