Search results
Results From The WOW.Com Content Network
In mathematics, a rotation of axes in two dimensions is a mapping from an xy - Cartesian coordinate system to an x′y′ -Cartesian coordinate system in which the origin is kept fixed and the x′ and y′ axes are obtained by rotating the x and y axes counterclockwise through an angle . A point P has coordinates ( x, y) with respect to the ...
The original and most common aspect of the Mercator projection for maps of the Earth is the normal aspect, for which the axis of the cylinder is the Earth's axis of rotation which passes through the North and South poles, and the contact circle is the Earth's equator.
A rotation in the plane can be formed by composing a pair of reflections. First reflect a point P to its image P′ on the other side of line L1. Then reflect P′ to its image P′′ on the other side of line L2. If lines L1 and L2 make an angle θ with one another, then points P and P′′ will make an angle 2θ around point O, the ...
Earth's rotation. Earth's rotation or Earth's spin is the rotation of planet Earth around its own axis, as well as changes in the orientation of the rotation axis in space. Earth rotates eastward, in prograde motion. As viewed from the northern polar star Polaris, Earth turns counterclockwise . The North Pole, also known as the Geographic North ...
The stereographic projection relates to the plane inversion in a simple way. Let P and Q be two points on the sphere with projections P ′ and Q ′ on the plane. Then P ′ and Q ′ are inversive images of each other in the image of the equatorial circle if and only if P and Q are reflections of each other in the equatorial plane.
Translation of axes. In mathematics, a translation of axes in two dimensions is a mapping from an xy - Cartesian coordinate system to an x'y' -Cartesian coordinate system in which the x' axis is parallel to the x axis and k units away, and the y' axis is parallel to the y axis and h units away. This means that the origin O' of the new ...
The sphere of rotations for the rotations that have a "horizontal" axis (in the xy plane). This visualization can be extended to a general rotation in 3-dimensional space. The identity rotation is a point, and a small angle of rotation about some axis can be represented as a point on a sphere with a small radius.
Rotation of an object in two dimensions around a point O. Rotation in mathematics is a concept originating in geometry. Any rotation is a motion of a certain space that preserves at least one point. It can describe, for example, the motion of a rigid body around a fixed point. Rotation can have a sign (as in the sign of an angle ): a clockwise ...