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The word "algebra" is a distortion of the Arabic title of a treatise by al-Khwārizmī about algebraic methods. In modern usage, algebra has several meanings. One use of the ...

The polar coordinates r (the radial coordinate) and theta (the angular coordinate, often called the polar angle) are defined in terms of Cartesian coordinates by x = ...

A closed box composed of three pairs of rectangular faces placed opposite each other and joined at right angles to each other, also known as a rectangular parallelepiped. The ...

Eigenvectors are a special set of vectors associated with a linear system of equations (i.e., a matrix equation) that are sometimes also known as characteristic vectors, ...

The icosahedral group I_h is the group of symmetries of the icosahedron and dodecahedron having order 120, equivalent to the group direct product A_5×Z_2 of the alternating ...

Lagrange's identity is the algebraic identity (sum_(k=1)^na_kb_k)^2=(sum_(k=1)^na_k^2)(sum_(k=1)^nb_k^2)-sum_(1<=k<j<=n)(a_kb_j-a_jb_k)^2 (1) (Mitrinović 1970, p. 41; Marsden ...

O_h is the point group of symmetries of the octahedron having order 48 that includes inversion. It is also the symmetry group of the cube, cuboctahedron, and truncated ...

A necessary and sufficient condition for a curve to be a helix is that the ratio of curvature to torsion be constant.

A curve on a surface whose tangents are always in the direction of principal curvature. The equation of the lines of curvature can be written |g_(11) g_(12) g_(22); b_(11) ...

A curve on the surface of a sphere. Examples include the baseball cover, Seiffert's spherical spiral, spherical helix, and spherical spiral.