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Cartesian coordinate system with a circle of radius 2 centered at the origin marked in red. The equation of a circle is (x − a)2 + (y − b)2 = r2 where a and b are the coordinates of the center (a, b) and r is the radius. Cartesian coordinates are named for René Descartes, whose invention of them in the 17th century revolutionized ...
Coordinate system. The spherical coordinate system is commonly used in physics. It assigns three numbers (known as coordinates) to every point in Euclidean space: radial distance r, polar angle θ ( theta ), and azimuthal angle φ ( phi ). The symbol ρ ( rho) is often used instead of r.
Right-hand rule. In mathematics and physics, the right-hand rule is a convention and a mnemonic, utilized to define the orientation of axes in three-dimensional space and to determine the direction of the cross product of two vectors, as well as to establish the direction of the force on a current-carrying conductor in a magnetic field.
Parabola. Part of a parabola (blue), with various features (other colours). The complete parabola has no endpoints. In this orientation, it extends infinitely to the left, right, and upward. The parabola is a member of the family of conic sections. In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U ...
Three-dimensional space. A representation of a three-dimensional Cartesian coordinate system with the x -axis pointing towards the observer. In geometry, a three-dimensional space ( 3D space, 3-space or, rarely, tri-dimensional space) is a mathematical space in which three values ( coordinates) are required to determine the position of a point.
In mechanics and geometry, the 3D rotation group, often denoted SO (3), is the group of all rotations about the origin of three-dimensional Euclidean space under the operation of composition. [ 1] By definition, a rotation about the origin is a transformation that preserves the origin, Euclidean distance (so it is an isometry ), and orientation ...
e. In physics, the Lorentz transformations are a six-parameter family of linear transformations from a coordinate frame in spacetime to another frame that moves at a constant velocity relative to the former. The respective inverse transformation is then parameterized by the negative of this velocity. The transformations are named after the ...
Rotation matrix. In linear algebra, a rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention below, the matrix. rotates points in the xy plane counterclockwise through an angle θ about the origin of a two-dimensional Cartesian coordinate system.