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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 about the rotation of Earth around its own axis, changes in the orientation of the rotation axis, and the history of the idea of a rotating Earth. Find out how Earth's rotation affects the length of a day, the seasons, the tides, and the shape of the planet.
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.
The angle θ and axis unit vector e define a rotation, concisely represented by the rotation vector θe.. In mathematics, the axis–angle representation parameterizes a rotation in a three-dimensional Euclidean space by two quantities: a unit vector e indicating the direction of an axis of rotation, and an angle of rotation θ describing the magnitude and sense (e.g., clockwise) of the ...
Rotation is the circular movement of an object around a central line, known as an axis of rotation. Learn about different types of rotation, such as spin, revolution, and principal rotations, and how to calculate rotation angle and axis using matrices.
Learn about the history, features and uses of the Mercator projection, a conformal cylindrical map projection presented by Gerardus Mercator in 1569. The Mercator projection is widely used for navigation, web maps and atlases, but it distorts the size and shape of landmasses near the poles.
Learn how to measure the average crown spread, the horizontal width of the foliage and branches of a tree, and other related parameters. Find out the largest recorded crown spreads and the methods to measure them.