Angle

two line bent at a point — A green angle formed by two red rays on the Cartesian coordinate system

In Euclidean geometry, an angle or plane angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.^[1] Two intersecting curves may also define an angle, which is the angle of the rays lying tangent to the respective curves at their point of intersection. Angles are also formed by the intersection of two planes; these are called dihedral angles. In any case, the resulting angle lies in a plane (spanned by the two rays or perpendicular to the line of plane-plane intersection).

The magnitude of an angle is called an angular measure or simply "angle". This measure, for an ordinary angle, is often visualized or defined using the arc of a circle centered at the vertex and lying between the sides. Two different angles may have the same measure, as in an isosceles triangle. "Angle" also denotes the angular sector, the infinite region of the plane bounded by the sides of an angle.^[2]^[3]^[a]

Angle of rotation is a measure conventionally defined as the ratio of a circular arc length to its radius, and may be a negative number; the arc is centered at the center of the rotation and delimited by any other point and its image after the rotation.

^ Sidorov 2001
^ Evgrafov, M. A. (2019-09-18). Analytic Functions. Courier Dover Publications. ISBN 978-0-486-84366-7.
^ Papadopoulos, Athanase (2012). Strasbourg Master Class on Geometry. European Mathematical Society. ISBN 978-3-03719-105-7.
^ D'Andrea, Francesco (2023-08-19). A Guide to Penrose Tilings. Springer Nature. ISBN 978-3-031-28428-1.
^ Bulboacǎ, Teodor; Joshi, Santosh B.; Goswami, Pranay (2019-07-08). Complex Analysis: Theory and Applications. Walter de Gruyter GmbH & Co KG. ISBN 978-3-11-065803-3.
^ Redei, L. (2014-07-15). Foundation of Euclidean and Non-Euclidean Geometries according to F. Klein. Elsevier. ISBN 978-1-4832-8270-1.

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[1] Sidorov 2001

[2] Evgrafov, M. A. (2019-09-18). Analytic Functions. Courier Dover Publications. ISBN 978-0-486-84366-7.

[3] Papadopoulos, Athanase (2012). Strasbourg Master Class on Geometry. European Mathematical Society. ISBN 978-3-03719-105-7.

[4] D'Andrea, Francesco (2023-08-19). A Guide to Penrose Tilings. Springer Nature. ISBN 978-3-031-28428-1.

[5] Bulboacǎ, Teodor; Joshi, Santosh B.; Goswami, Pranay (2019-07-08). Complex Analysis: Theory and Applications. Walter de Gruyter GmbH & Co KG. ISBN 978-3-11-065803-3.

[6] Redei, L. (2014-07-15). Foundation of Euclidean and Non-Euclidean Geometries according to F. Klein. Elsevier. ISBN 978-1-4832-8270-1.

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