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Learn how to rotate a Cartesian coordinate system by an angle and transform the coordinates of points and curves. See examples, formulas, and applications of rotation of axes in two dimensions.
A rotation matrix is a matrix that rotates vectors or points in Euclidean space. Learn the definition, properties, formulas, and examples of rotation matrices in two and three dimensions.
Learn how to represent linear and non-linear transformations by matrices in linear algebra. Find examples of common transformations in two and three dimensions, such as rotation, scaling, shearing, reflection, and projection.
Learn about the concept of rotation in geometry and algebra, and how it can be represented in different dimensions and formalisms. Find out the definitions, properties, and examples of rotations, as well as their applications in physics and mechanics.
Learn how to express a rotation in three dimensions as a mathematical transformation using different methods, such as rotation matrix, Euler axis and angle, and Euler rotations. Compare the properties, advantages, and disadvantages of each formalism.
Learn about the spherical coordinate system for three-dimensional space, where the position of a point is specified by radial distance, polar angle, and azimuthal angle. Compare different conventions and terminologies for these angles, such as colatitude, elevation, and longitude.
Curl is a vector operator that describes the infinitesimal circulation of a vector field in three-dimensional space. Learn how to define and use curl in different ways, and how it relates to other vector calculus concepts such as gradient, divergence, and Stokes' theorem.
atan2 is a 2-argument arctangent function that returns the angle between the positive x-axis and the ray from the origin to the point (x, y). Learn how it differs from arctan, how it is used in computing and mathematics, and how it relates to complex numbers and differential geometry.