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A Cartesian coordinate system in two dimensions (also called a rectangular coordinate system or an orthogonal coordinate system [8]) is defined by an ordered pair of perpendicular lines (axes), a single unit of length for both axes, and an orientation for each axis. The point where the axes meet is taken as the origin for both, thus turning ...
A Cartesian coordinate surface in this space is a coordinate plane; for example z = 0 defines the x-y plane. In the same space, the coordinate surface r = 1 in spherical coordinates is the surface of a unit sphere, which is curved. The formalism of curvilinear coordinates provides a unified and general description of the standard coordinate ...
This is a suitable choice of generalized coordinate for the system. Only one coordinate is needed instead of two, because the position of the bead can be parameterized by one number, s, and the constraint equation connects the two coordinates x and y; either one is determined from the other. The constraint force is the reaction force the wire ...
The plane of the Earth's orbit about the Sun is called the ecliptic, and the plane perpendicular to the rotation axis of the Earth is the equatorial plane. The angle between the ecliptic and the equatorial plane is called variously the axial tilt, the obliquity, or the inclination of the ecliptic, and it is conventionally denoted by i.
Points in the polar coordinate system with pole O and polar axis L. In green, the point with radial coordinate 3 and angular coordinate 60 degrees or (3, 60°). In blue, the point (4, 210°). In mathematics, the polar coordinate system specifies a given point in a plane by using a distance and an angle as its two coordinates. These are
By definition, the positions of the Tropic of Cancer, Tropic of Capricorn, Arctic Circle and Antarctic Circle all depend on the tilt of the Earth's axis relative to the plane of its orbit around the Sun (the "obliquity of the ecliptic"). If the Earth were "upright" (its axis at right angles to the orbital plane) there would be no Arctic ...
The plane of rotation is orthogonal to this plane, and the rotation can be said to take place in this plane. For example the following matrix fixes the xy-plane: points in that plane and only in that plane are unchanged. The plane of rotation is the zw-plane, points in this plane are rotated through an angle θ.
A projective plane is defined axiomatically as an incidence structure, in terms of a set P of points, a set L of lines, and an incidence relation I that determines which points lie on which lines. As P and L are only sets one can interchange their roles and define a plane dual structure. By interchanging the role of "points" and "lines" in C ...
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