Euler square

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• Euler's three-body problem — In physics and astronomy, Euler s three body problem is to solve for the motion of a particle that is acted upon by the gravitational field of two other point masses that are either fixed in space or move in circular coplanar orbits about their… …   Wikipedia

• Euler's four-square identity — In mathematics, Euler s four square identity says that the product of two numbers, each of which being a sum of four squares, is itself a sum of four squares. Specifically::(a 1^2+a 2^2+a 3^2+a 4^2)(b 1^2+b 2^2+b 3^2+b 4^2)=,::(a 1 b 1 a 2 b 2 a… …   Wikipedia

• Euler's identity — [ 300px|thumb|right|The exponential function e z can be defined as the limit of nowrap|(1 + z / N ) N , as N approaches infinity, and thus e iπ is the limit of nowrap|(1 + iπ/N ) N . In this animation N takes various increasing values from 1 to… …   Wikipedia

• Euler–Maclaurin formula — In mathematics, the Euler–Maclaurin formula provides a powerful connection between integrals (see calculus) and sums. It can be used to approximate integrals by finite sums, or conversely to evaluate finite sums and infinite series using… …   Wikipedia

• Euler product — In number theory, an Euler product is an infinite product expansion, indexed by prime numbers p , of a Dirichlet series. The name arose from the case of the Riemann zeta function, where such a product representation was proved by Euler.In general …   Wikipedia

• Euler's criterion — In mathematics, Euler s criterion is used in determining in number theory whether a given integer is a quadratic residue modulo a prime. DefinitionEuler s criterion states: Let p be an odd prime and a an integer coprime to p . Then a is a… …   Wikipedia

• Euler function — For other meanings, see List of topics named after Leonhard Euler .In mathematics, the Euler function is given by:phi(q)=prod {k=1}^infty (1 q^k).Named after Leonhard Euler, it is a prototypical example of a q series, a modular form, and provides …   Wikipedia

• Square number — In mathematics, a square number, sometimes also called a perfect square, is an integer that can be written as the square of some other integer; in other words, it is the product of some integer with itself. So, for example, 9 is a square number,… …   Wikipedia

• Square root of 2 — The square root of 2, also known as Pythagoras constant, often denoted by:sqrt{2} or √2but can also be written as:2^{1/2},,is the positive real number that, when multiplied by itself, gives the number 2. Its numerical value approximated to 65… …   Wikipedia

• Square-free integer — In mathematics, a square free, or quadratfrei, integer is one divisible by no perfect square, except 1. For example, 10 is square free but 18 is not, as it is divisible by 9 = 32. The smallest square free numbers are :1, 2, 3, 5, 6, 7, 10, 11, 13 …   Wikipedia

• Euler's formula — 1. Math. the theorem that ei x = cos(x) + i sin(x). 2. Mech. a formula for determining the maximum load that can be applied to a given column without causing it to buckle. [1945 50; named after L. EULER] * * * Either of two important mathematical …   Universalium