Archimedean Spiral Polar
Archimedean means of or pertaining to or named in honor of the Greek mathematician Archimedes and may refer to: Mathematics * Archimedean absolute value *Archimedean circle * Archimedean constant * Archimedean copula *Archimedean field *Archimedean group * Archimedean point *Archimedean property *Archimedean solid *Archimedean spiral *Archimedean tiling Other uses *Archimedean screw *Claw of Archimedes *The Archimedeans, the mathematical society of the University of Cambridge * Archimedean Dynasty *Archimedean Upper Conservatory See also * Archimedes (other) Archimedes was a celebrated mathematician and engineer of ancient Greece. Archimedes may also refer to: People Given name * Archimedes of Tralles, ancient Greek writer * Arquimedes Caminero (born 1987), Dominican baseball player * Archimedes P ...

Archimedes
Archimedes of Syracuse (;; ) was a Greek mathematician, physicist, engineer, astronomer, and inventor from the ancient city of Syracuse in Sicily. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Considered the greatest mathematician of ancient history, and one of the greatest of all time,* * * * * * * * * * Archimedes anticipated modern calculus and analysis by applying the concept of the infinitely small and the method of exhaustion to derive and rigorously prove a range of geometrical theorems. These include the area of a circle, the surface area and volume of a sphere, the area of an ellipse, the area under a parabola, the volume of a segment of a paraboloid of revolution, the volume of a segment of a hyperboloid of revolution, and the area of a spiral. Heath, Thomas L. 1897. ''Works of Archimedes''. Archimedes' other mathematical achievements include deriving an approximation of pi, de ...
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Archimedean Absolute Value
In algebra, an absolute value (also called a valuation, magnitude, or norm, although "norm" usually refers to a specific kind of absolute value on a field) is a function which measures the "size" of elements in a field or integral domain. More precisely, if ''D'' is an integral domain, then an absolute value is any mapping , x, from ''D'' to the real numbers R satisfying: It follows from these axioms that , 1,  = 1 and , -1,  = 1. Furthermore, for every positive integer ''n'', :, ''n'',  = , 1 + 1 + ... + 1 (''n'' times),  = , −1 − 1 − ... − 1 (''n'' times),  ≤ ''n''. The classical " absolute value" is one in which, for example, , 2, =2, but many other functions fulfill the requirements stated above, for instance the square root of the classical absolute value (but not the square thereof). An absolute value induces a metric (and thus a topology) by d(f,g) = ...
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Archimedean Circle
In geometry, an Archimedean circle is any circle constructed from an arbelos that has the same radius as each of Archimedes' twin circles. If the arbelos is normed such that the diameter of its outer (largest) half circle has a length of 1 and ''r'' denotes the radiius of any of the inner half circles, then the radius ''ρ'' of such an Archimedean circle is given by :\rho=\fracr\left(1-r\right), There are over fifty different known ways to construct Archimedean circles. Origin An Archimedean circle was first constructed by Archimedes in his ''Book of Lemmas''. In his book, he constructed what is now known as Archimedes' twin circles. Radius If a and b are the radii of the small semicircles of the arbelos, the radius of an Archimedean circle is equal to :R = \frac This radius is thus \frac 1R = \frac 1a + \frac 1b. The Archimedean circle with center C (as in the figure at right) is tangent to the tangents from the centers of the small semicircles to the other small semic ...
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Archimedean Constant
The number (; spelled out as "pi") is a mathematical constant that is the ratio of a circle's circumference to its diameter, approximately equal to 3.14159. The number appears in many formulas across mathematics and physics. It is an irrational number, meaning that it cannot be expressed exactly as a ratio of two integers, although fractions such as \tfrac are commonly used to approximate it. Consequently, its decimal representation never ends, nor enters a permanently repeating pattern. It is a transcendental number, meaning that it cannot be a solution of an equation involving only sums, products, powers, and integers. The transcendence of implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straightedge. The decimal digits of appear to be randomly distributed, but no proof of this conjecture has been found. For thousands of years, mathematicians have attempted to extend their understanding of , sometimes by computin ...
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