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Multiplication table from 1 to 10 drawn to scale with the upper-right half labeled with prime factorisations In mathematics , a multiplication table (sometimes, less formally, a times table ) is a mathematical table used to define a multiplication operation for an algebraic system.
Patchouli (also spelled patchouly or pachouli) (/ p ə ˈ tʃ uː l i /; Pogostemon cablin) is a species of flowering plant in the family Lamiaceae, commonly called the mint or deadnettle family. The plant grows as a bushy perennial herb , with erect stems reaching up to 75 centimetres (30 in) in height and bearing small, pale, pink-white flowers.
Patchoulol or patchouli alcohol (C 15 H 26 O) is a sesquiterpene alcohol found in patchouli. [1] Patchouli oil is an important material in perfumery. The (−)-optical isomer is one of the organic compounds responsible for the typical patchouli scent. Patchoulol is obtained by fermentation of leaves of Pogostemon cablin. [2]
As shown in Scheme 1, the first steps in the synthesis created the bicyclo[5.3.1]undecane AB ring system of Taxol. Reaction of epoxide 1 with tert-butyllithium removed the acidic α-epoxide proton, leading to an elimination reaction and simultaneous ring-opening of the epoxide to give allylic alcohol 2 .
Korean mint leaf. A. rugosa is a perennial plant growing up to 40–100 centimetres (16–39 inches) tall, with square stalks that branch at the upper part. [8] The oval-cordate leaves are oppositely arranged, 5–10 cm (2–4 in) long and 3–7 cm (1 + 1 ⁄ 4 – 2 + 3 ⁄ 4 in) broad, with coarsely serrated margins. [8]
The group {1, −1} above and the cyclic group of order 3 under ordinary multiplication are both examples of abelian groups, and inspection of the symmetry of their Cayley tables verifies this. In contrast, the smallest non-abelian group, the dihedral group of order 6, does not have a symmetric Cayley table.
The History of Mathematical Tables: from Sumer to Spreadsheets is an edited volume in the history of mathematics on mathematical tables.It was edited by Martin Campbell-Kelly, Mary Croarken, Raymond Flood, and Eleanor Robson, developed out of the presentations at a conference on the subject organised in 2001 by the British Society for the History of Mathematics, [1] [2] and published in 2003 ...
Today, a more standard phrasing of Archimedes' proposition is that the partial sums of the series 1 + 1 / 4 + 1 / 16 + ⋯ are: + + + + = +. This form can be proved by multiplying both sides by 1 − 1 / 4 and observing that all but the first and the last of the terms on the left-hand side of the equation cancel in pairs.
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