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Enantiotopic groups are identical and indistinguishable except in chiral environments. For instance, the CH 2 hydrogens in ethanol (CH 3 CH 2 OH) are normally enantiotopic, but can be made different (diastereotopic) if combined with a chiral center, for instance by conversion to an ester of a chiral carboxylic acid such as lactic acid, or if coordinated to a chiral metal center, or if ...
One example is [Ru(NH 3) 5 (SMeEt)] 2+. The complex cis-VOCl 2 (SMeEt) 2 exists as meso- and a pair of enantiomers. [7] In complexes of thioethers of the type S(CH 2 R) 2 (R ≠ H), the methylene protons are diastereotopic. Examination of the NMR spectra of such complexes reveal that they undergo inversion at sulfur, without dissociation of the ...
Two intersecting lines. In Euclidean geometry, the intersection of a line and a line can be the empty set, a point, or another line. Distinguishing these cases and finding the intersection have uses, for example, in computer graphics, motion planning, and collision detection.
Symmetrical norbornanes and similarly rigid compounds (e.g. 7-oxabicyclo[2.2.1]heptane) also show complex signals for the ethylene fragments, made more complicated by additional splitting by the bridgehead protons. Reich gives several additional examples of magnetic inequivalence in acyclic and cyclic systems containing H 2 C-CH 2 fragments. [3]
The three possible plane-line relationships in three dimensions. (Shown in each case is only a portion of the plane, which extends infinitely far.) In analytic geometry, the intersection of a line and a plane in three-dimensional space can be the empty set, a point, or a line. It is the entire line if that line is embedded in the plane, and is ...
The simplest case in Euclidean geometry is the line–line intersection between two distinct lines, which either is one point (sometimes called a vertex) or does not exist (if the lines are parallel). Other types of geometric intersection include: Line–plane intersection; Line–sphere intersection; Intersection of a polyhedron with a line
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An arrangement in which the midpoint of all the spheres lie on a single straight line is called a sausage packing, as the convex hull has a sausage-like shape.An approximate example in real life is the packing of tennis balls in a tube, though the ends must be rounded for the tube to coincide with the actual convex hull.