By James Stuart Tanton
A one-volume encyclopedia designed for prime university via early students. With greater than 1,000 entries, greater than a hundred twenty five images and illustrations, it unites disparate principles and gives the that means, heritage, context, and relevance in the back of every one one..
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Extra resources for Encyclopedia of Mathematics
At the turn of the century, Argand independently began to interpret the complex number i geometrically as a rotation through 90°. He expounded on the convenience and fruitfulness of this idea in a small book, Essai sur une manière de représenter les quantités imaginaires dans les constructions géometriques (Essay on a method for representing imaginary quantities through a geometric construction), which he published privately, at his own expense, in 1806. He never wrote his name in the piece, and so it was impossible to identify the author.
For example, that (a * b) * (c * d) equals (a * (b * c)) * d can be established with two applications of the fundamental relation as follows: (a * b) * (c * d) = ((a * b) * c) * d = (a * (b * c)) * d. As a consequence, if the associative property holds for a given set, parentheses may be omitted when writing products: one can simply write a * b * c * d, for instance, without concern for confusion. These considerations break down, however, if the expression under consideration contains an infinite number of terms.
Archytas of Tarentum (ca. ) Greek Geometry, Philosophy The Greek scholar Archytas of Tarentum was the first to provide a solution to the classic DUPLICATING THE CUBE problem of antiquity. By reducing the challenge to one of constructing certain ratios and proportions, Archytas developed a geometric construct that involved rotating semicircles through certain angles in three-dimensional space to produce a length essentially equivalent to the construct of the cube root of two. ) Although his innovative solution is certainly correct, it uses tools beyond what is permissible with straightedge and compass alone.