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Al-Jabr (Arabic: الجبر), also known as The Compendious Book on Calculation by Completion and Balancing (Arabic: الكتاب المختصر في حساب الجبر والمقابلة, al-Kitāb al-Mukhtaṣar fī Ḥisāb al-Jabr wal-Muqābalah; [b] or Latin: Liber Algebræ et Almucabola), is an Arabic mathematical treatise on algebra written in Baghdad around 820 by the Persian polymath ...
where v 1, v 2, ..., v k are in S, and a 1, a 2, ..., a k are in F form a linear subspace called the span of S. The span of S is also the intersection of all linear subspaces containing S. In other words, it is the smallest (for the inclusion relation) linear subspace containing S. A set of vectors is linearly independent if none is in the span ...
The algebraic equation + + = describes a sphere at the origin with a radius of 1. One application, found in geometry, is the use of algebraic statements to describe geometric figures. For example, the equation y = 3 x − 7 {\displaystyle y=3x-7} describes a line in two-dimensional space while the equation x 2 + y 2 + z 2 = 1 {\displaystyle x ...
For the above isosceles triangle with unit sides and angle , the area 1 / 2 × base × height is calculated in two orientations. When upright, the area is sin θ cos θ {\displaystyle \sin \theta \cos \theta } .
Barrack 3 of the guard of Stalag VII-A in 2013. After the liberation Stalag VII-A was turned into Civilian Internment Camp #6 for 12,000 German men and women suspected of criminal activity for the Nazi regime. Later the camp was turned into a new district of the town called Moosburg-Neustadt. [1] One of the old huts has been restored. [citation ...
The plan was to build the plant along the Gulf of Kutch, an inlet of the Arabian Sea that provides a living for fishing clans that harvest the coast’s rich marine life.
Jake Joseph Paul (born January 17, 1997) is an American professional boxer, influencer and actor.He began his career posting videos on Vine in September 2013 and had amassed 5.3 million followers and 2 billion views before the app was discontinued.
However, these counterexamples rely on −1 having a square root. If we take a field where −1 has no square root, and every polynomial of degree n ∈ I has a root, where I is any fixed infinite set of odd numbers, then every polynomial f(x) of odd degree has a root (since (x 2 + 1) k f(x) has a root, where k is chosen so that deg(f) + 2k ∈ I).