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convex angle (Definition)

A positive angle is convex if it is at most 180 degrees, i.e. $ \pi$ radians. Cf. the convex set.

A convex angle $ \alpha$ is

  • straight if $ \alpha = 180^{\mathrm{o}}$,
  • obtuse if $ 90^{\mathrm{o}} < \alpha < 180^{\mathrm{o}}$,
  • right if $ \alpha = 90^{\mathrm{o}}$,
  • acute if $ 0^{\mathrm{o}} < \alpha < 90^{\mathrm{o}}$,
  • skew if it is acute or obtuse.

Note. The angle between two curves which intersect each other in a point $ P$ means the angle between the tangent lines of the curves in $ P$; such angle may always be chosen acute or right.



"convex angle" is owned by pahio.
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See Also: quadrant, solid angle, orthogonal curves, complementary angles, level curve

Also defines:  straight angle, obtuse angle, right angle, acute angle, straight, obtuse, right, acute
Keywords:  convex

Attachments:
radian (Definition) by Mravinci
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Cross-references: curves, tangent lines, point, intersect, convex set, radians, angle, positive
There are 380 references to this entry.

This is version 13 of convex angle, born on 2004-11-08, modified 2006-08-16.
Object id is 6456, canonical name is ConvexAngle.
Accessed 16479 times total.

Classification:
AMS MSC: 51M04 (Geometry :: Real and complex geometry :: Elementary problems in Euclidean geometries)
Pending Errata and Addenda
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