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.
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.
Coordination complexA coordination complex is a chemical compound consisting of a central atom or ion, which is usually metallic and is called the coordination centre, and a surrounding array of bound molecules or ions, that are in turn known as ligands or complexing agents. Many metal-containing compounds, especially those that include transition metals (elements like titanium that belong to the periodic table's d-block), are coordination complexes. Coordination complexes are so pervasive that their structures and reactions are described in many ways, sometimes confusingly.
HalideIn chemistry, a halide (rarely halogenide) is a binary chemical compound, of which one part is a halogen atom and the other part is an element or radical that is less electronegative (or more electropositive) than the halogen, to make a fluoride, chloride, bromide, iodide, astatide, or theoretically tennesside compound. The alkali metals combine directly with halogens under appropriate conditions forming halides of the general formula, MX (X = F, Cl, Br or I). Many salts are halides; the hal- syllable in halide and halite reflects this correlation.
Octahedral molecular geometryIn chemistry, octahedral molecular geometry, also called square bipyramidal, describes the shape of compounds with six atoms or groups of atoms or ligands symmetrically arranged around a central atom, defining the vertices of an octahedron. The octahedron has eight faces, hence the prefix octa. The octahedron is one of the Platonic solids, although octahedral molecules typically have an atom in their centre and no bonds between the ligand atoms. A perfect octahedron belongs to the point group Oh.
LigandIn coordination chemistry, a ligand is an ion or molecule with a functional group that binds to a central metal atom to form a coordination complex. The bonding with the metal generally involves formal donation of one or more of the ligand's electron pairs, often through Lewis bases. The nature of metal–ligand bonding can range from covalent to ionic. Furthermore, the metal–ligand bond order can range from one to three. Ligands are viewed as Lewis bases, although rare cases are known to involve Lewis acidic "ligands".
Catalytic cycleIn chemistry, a catalytic cycle is a multistep reaction mechanism that involves a catalyst. The catalytic cycle is the main method for describing the role of catalysts in biochemistry, organometallic chemistry, bioinorganic chemistry, materials science, etc. Since catalysts are regenerated, catalytic cycles are usually written as a sequence of chemical reactions in the form of a loop. In such loops, the initial step entails binding of one or more reactants by the catalyst, and the final step is the release of the product and regeneration of the catalyst.
Dicobalt octacarbonylDicobalt octacarbonyl is an organocobalt compound with composition . This metal carbonyl is used as a reagent and catalyst in organometallic chemistry and organic synthesis, and is central to much known organocobalt chemistry. It is the parent member of a family of hydroformylation catalysts. Each molecule consists of two cobalt atoms bound to eight carbon monoxide ligands, although multiple structural isomers are known. Some of the carbonyl ligands are labile. Dicobalt octacarbonyl an orange-colored, pyrophoric solid.
ChlorineChlorine is a chemical element with the symbol Cl and atomic number 17. The second-lightest of the halogens, it appears between fluorine and bromine in the periodic table and its properties are mostly intermediate between them. Chlorine is a yellow-green gas at room temperature. It is an extremely reactive element and a strong oxidising agent: among the elements, it has the highest electron affinity and the third-highest electronegativity on the revised Pauling scale, behind only oxygen and fluorine.
