Organoboron chemistryOrganoboron chemistry or organoborane chemistry is the chemistry of organoboron compounds or organoboranes, which are chemical compounds of boron and carbon that are organic derivatives of borane (BH3), for example trialkyl boranes. . Organoboron compounds are important reagents in organic chemistry enabling many chemical transformations, the most important ones being hydroboration and carboboration. Reactions of organoborates and boranes involve the transfer of a nucleophilic group attached to boron to an electrophilic center either inter- or intramolecularly.
Similarity (geometry)In Euclidean geometry, two objects are similar if they have the same shape, or if one has the same shape as the mirror image of the other. More precisely, one can be obtained from the other by uniformly scaling (enlarging or reducing), possibly with additional translation, rotation and reflection. This means that either object can be rescaled, repositioned, and reflected, so as to coincide precisely with the other object. If two objects are similar, each is congruent to the result of a particular uniform scaling of the other.
Haloform reactionIn chemistry, the haloform reaction is a chemical reaction in which a haloform (, where X is a halogen) is produced by the exhaustive halogenation of an acetyl group (, where R can be either a hydrogen atom, an alkyl or an aryl group), in the presence of a base. The reaction can be used to transform acetyl groups into carboxyl groups () or to produce chloroform (), bromoform (), or iodoform (). Note that fluoroform () can't be prepared in this way. In the first step, the halogen dis-proportionates in the presence of hydroxide to give the halide and hypohalite.
Self-similarityIn mathematics, a self-similar object is exactly or approximately similar to a part of itself (i.e., the whole has the same shape as one or more of the parts). Many objects in the real world, such as coastlines, are statistically self-similar: parts of them show the same statistical properties at many scales. Self-similarity is a typical property of fractals. Scale invariance is an exact form of self-similarity where at any magnification there is a smaller piece of the object that is similar to the whole.
Plane curveIn mathematics, a plane curve is a curve in a plane that may be either a Euclidean plane, an affine plane or a projective plane. The most frequently studied cases are smooth plane curves (including piecewise smooth plane curves), and algebraic plane curves. Plane curves also include the Jordan curves (curves that enclose a region of the plane but need not be smooth) and the graphs of continuous functions. A plane curve can often be represented in Cartesian coordinates by an implicit equation of the form for some specific function f.
Complex planeIn mathematics, the complex plane is the plane formed by the complex numbers, with a Cartesian coordinate system such that the x-axis, called the real axis, is formed by the real numbers, and the y-axis, called the imaginary axis, is formed by the imaginary numbers. The complex plane allows a geometric interpretation of complex numbers. Under addition, they add like vectors.
Plane (mathematics)In mathematics, a plane is a two-dimensional space or flat surface that extends indefinitely. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space. When working exclusively in two-dimensional Euclidean space, the definite article is used, so the Euclidean plane refers to the whole space. Many fundamental tasks in mathematics, geometry, trigonometry, graph theory, and graphing are performed in a two-dimensional or planar space.
