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Pages in category "Pi algorithms" The following 17 pages are in this category, out of 17 total. This list may not reflect recent changes. A.
Sigma and pi bonds in graphene. Sigma bonds result from an overlap of sp 2 hybrid orbitals, whereas pi bonds emerge from tunneling between the protruding p z orbitals. For clarity, only one p z orbital is shown with its three nearest neighbors.
Erich Hückel proposed a representation of the double bond as a combination of a sigma bond plus a pi bond. [ 7 ] [ 8 ] [ 9 ] The σ-π representation is the better-known one, and it is the one found in most textbooks since the late-20th century.
According to the sigma bond rule, the number of sigma bonds in a molecule is equivalent to the number of atoms plus the number of rings minus one. N σ = N atoms + N rings − 1 This rule is a special-case application of the Euler characteristic of the graph which represents the molecule.
In mathematics, Machin-like formulas are a popular technique for computing π (the ratio of the circumference to the diameter of a circle) to a large number of digits.They are generalizations of John Machin's formula from 1706:
Using the P function mentioned above, the simplest known formula for π is for s = 1, but m > 1. Many now-discovered formulae are known for b as an exponent of 2 or 3 and m as an exponent of 2 or it some other factor-rich value, but where several of the terms of sequence A are zero.
The more positive is the value of pEDA the more pi-electron donating is a substituent. The more negative pEDA, the more pi-electron withdrawing is the substituent (see the table below). The pEDA parameter for a given substituent is calculated by means of quantum chemistry methods. The model molecule is the monosubstituted benzene.
In mathematics, the Leibniz formula for π, named after Gottfried Wilhelm Leibniz, states that = + + = = +,. an alternating series.. It is sometimes called the Madhava–Leibniz series as it was first discovered by the Indian mathematician Madhava of Sangamagrama or his followers in the 14th–15th century (see Madhava series), [1] and was later independently rediscovered by James Gregory in ...