In geometry, an angle is formed by two lines that meet at a point. Each line is called a side of the angle, and the point they share is called the vertex of the angle. The term angle is used to denote both geometric figures and their size or magnitude as associated quantity. Angular measure or measure of angle are sometimes used to distinguish between the measure of the quantity and figure itself. The measurement of angles is intrinsically linked with circles and rotation, and this is often visualized or defined using the arc of a circle centered at the vertex and lying between the sides.
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In this Dossier
- ⭐ Core Definition: Plane angle
- Plane angle in the context of Edge (geometry)
- Plane angle in the context of Turn (unit)
- Plane angle in the context of Cylindrical coordinate system
Plane angle in the context of Edge (geometry)
In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope. In a polygon, an edge is a line segment on the boundary, and is often called a polygon side. In a polyhedron or more generally a polytope, an edge is a line segment where two faces (or polyhedron sides) meet. A segment joining two vertices while passing through the interior or exterior is not an edge but instead is called a diagonal.
An edge may also be an infinite line separating two half-planes.The sides of a plane angle are semi-infinite half-lines (or rays).
View the full Wikipedia page for Edge (geometry)Plane angle in the context of Turn (unit)
The turn (symbol tr or pla) is a unit of plane angle measurement that is the measure of a complete angle—the angle subtended by a complete circle at its center. One turn is equal to 2π radians, 360 degrees or 400 gradians. As an angular unit, one turn also corresponds to one cycle (symbol cyc or c) or to one revolution (symbol rev or r). Common related units of frequency are cycles per second (cps) and revolutions per minute (rpm). The angular unit of the turn is useful in connection with, among other things, electromagnetic coils (e.g., transformers), rotating objects, and the winding number of curves. Divisions of a turn include the half-turn and quarter-turn, spanning a straight angle and a right angle, respectively; metric prefixes can also be used as in, e.g., centiturns (ctr), milliturns (mtr), etc.
In the ISQ, an arbitrary "number of turns" (also known as "number of revolutions" or "number of cycles") is formalized as a dimensionless quantity called rotation, defined as the ratio of a given angle and a full turn. It is represented by the symbol N.
View the full Wikipedia page for Turn (unit)Plane angle in the context of Cylindrical coordinate system
A cylindrical coordinate system is a three-dimensional coordinate system that specifies point positions around a main axis (a chosen directed line) and an auxiliary axis (a reference ray). The three cylindrical coordinates are: the point perpendicular distance ρ from the main axis; the point signed distance z along the main axis from a chosen origin; and the plane angle φ of the point projection on a reference plane (passing through the origin and perpendicular to the main axis)
The main axis is variously called the cylindrical or longitudinal axis. The auxiliary axis is called the polar axis, which lies in the reference plane, starting at the origin, and pointing in the reference direction.Other directions perpendicular to the longitudinal axis are called radial lines.
View the full Wikipedia page for Cylindrical coordinate system