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Since C = 2πr, the circumference of a unit circle is 2π. In mathematics, a unit circle is a circle of unit radius—that is, a radius of 1. [1] Frequently, especially in trigonometry, the unit circle is the circle of radius 1 centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane.
In mathematics, the circle group, denoted by or , is the multiplicative group of all complex numbers with absolute value 1, that is, the unit circle in the complex plane or simply the unit complex numbers[1] The circle group forms a subgroup of , the multiplicative group of all nonzero complex numbers. Since is abelian, it follows ...
Group theory has three main historical sources: number theory, the theory of algebraic equations, and geometry. The number-theoretic strand was begun by Leonhard Euler, and developed by Gauss's work on modular arithmetic and additive and multiplicative groups related to quadratic fields.
An atom (or ion) whose oxidation number increases in a redox reaction is said to be oxidized (and is called a reducing agent). It is accomplished by loss of one or more electrons. The atom whose oxidation number decreases gains (receives) one or more electrons and is said to be reduced. This relation can be remembered by the following mnemonics.
The periodic table, also known as the periodic table of the elements, is an ordered arrangement of the chemical elements into rows ("periods") and columns ("groups"). It is an icon of chemistry and is widely used in physics and other sciences. It is a depiction of the periodic law, which states that when the elements are arranged in order of ...
In mathematics, specifically in group theory, the Prüfer p-group or the p-quasicyclic group or p∞ -group, Z (p∞), for a prime number p is the unique p -group in which every element has p different p -th roots. The Prüfer p -groups are countable abelian groups that are important in the classification of infinite abelian groups: they (along ...
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The quotient group is isomorphic to the circle group, the group of complex numbers of absolute value 1 under multiplication, or correspondingly, the group of rotations in 2D about the origin, that is, the special orthogonal group . An isomorphism is given by (see Euler's identity).