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Leonhard Euler (/ ˈ ɔɪ l ər / OY-lər; [b] German: [ˈleːɔnhaʁt ˈʔɔʏlɐ] ⓘ, Swiss Standard German: [ˈleːɔnhart ˈɔʏlər]; 15 April 1707 – 18 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician, and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in many other branches of ...
Rhineland-Palatinate. Established. 20 June 1975. (49 years ago) (1975-06-20) Named for. Kaiserslautern. The Kaiserslautern Military Community (KMC) is an American military community in and around Kaiserslautern, Germany, supporting United States Armed Forces and NATO installations, such as the Ramstein Air Base, Landstuhl Regional Medical ...
v. t. e. Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. Euler's formula states that, for any real number x, one has where e is the base of the natural logarithm, i is the imaginary ...
Euler also made contributions to the understanding of planar graphs. He introduced a formula governing the relationship between the number of edges, vertices, and faces of a convex polyhedron. Given such a polyhedron, the alternating sum of vertices, edges and faces equals a constant: V − E + F = 2.
Ramstein AB is part of the Kaiserslautern Military Community (KMC), where around 54,000 American service members and over 5,400 U.S. civilian employees live and work. U.S. organizations in the KMC also employ the services of more than 6,200 German workers. Air Force units in the KMC alone employ almost 9,800 military members, who are ...
Foreign Military Sales (FMS) is a security assistance program of the United States government to facilitate the purchase of U.S. arms, defense equipment, design and construction services, and military training to foreign governments. [1] FMS is a government-to-government program where the United States Department of Defense through the Defense ...
In mathematics, Euler's identity[note 1] (also known as Euler's equation) is the equality where. is pi, the ratio of the circumference of a circle to its diameter. Euler's identity is named after the Swiss mathematician Leonhard Euler. It is a special case of Euler's formula when evaluated for .
The number of Euler angles needed to represent the group SO(n) is n(n − 1)/2, equal to the number of planes containing two distinct coordinate axes in n-dimensional Euclidean space. In SO(4) a rotation matrix is defined by two unit quaternions , and therefore has six degrees of freedom, three from each quaternion.