PlanarAngle

PlanarAngle[p{q1,q2}]

gives the angle between the halflines from p through q1 and q2.

PlanarAngle[{q1,p,q2}]

gives the angle at p formed by the triangle with vertex points p, q1 and q2.

PlanarAngle[,"spec"]

gives the angle specified by "spec".

Details

  • PlanarAngle is also known as angle.
  • PlanarAngle[p{q1,q2}] gives the length of the arc of the unit circle Circle[p] delimited by the half-line from p through q1 on the left and the half-line from p to q2 on the right.
  • Two halflines from p through q1 and q2 delimit two angles α1 and α2 at p.
  • The following specifications "spec" can be given:
  • "Counterclockwise"angle formed by the counterclockwise rotation from q1 to q2
    "Clockwise"angle formed by the clockwise rotation from q1 to q2
  • PlanarAngle[p{q1,q2},"Counterclockwise"] is equivalent to PlanarAngle[p{q1,q2}].
  • PlanarAngle[p{q1,q2},"Clockwise"] is equivalent to PlanarAngle[p{q2,q1}].
  • PlanarAngle[{q1,p,q2}] is the angle subtended by the line segment q1 q2 from p.
  • The triangle with vertex points q1, p and q2 defines three angles α1, α2 and α3 at p.
  • The following specifications "spec" can be given:
  • "Interior"interior (inside) angle of the triangle at p
    "Exterior"exterior angle of the triangle at p
    "FullExterior"full exterior angle of the triangle at p
  • PlanarAngle[{q1,p,q2},"Interior"] is equivalent to PlanarAngle[{q1,p,q2}].
  • PlanarAngle[{q1,p,q2},"Exterior"] is equivalent to π-PlanarAngle[{q1,p,q2}].
  • PlanarAngle[{q1,p,q2},"FullExterior"] is equivalent to 2π-PlanarAngle[{q1,p,q2}].
  • With the specification "Interior", "Exterior" or "FullExterior", PlanarAngle[p{q1,q2},"spec"] is taken to be PlanarAngle[{q1,p,q2},"spec"].
  • With the specification "Counterclockwise" or "Clockwise", PlanarAngle[{q1,p,q2},"spec"] is taken to be PlanarAngle[p{q1,q2}, "spec"].
  • PlanarAngle can be used with symbolic points in GeometricScene.

Examples

open all close all

Basic Examples  (2)

The angle between the halflines from {0,0} through {1,1} and {1,0}:

In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=

The angle formed by a triangle at origin:

In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=

Scope  (7)

Applications  (6)

Properties & Relations  (7)

Possible Issues  (1)

Introduced in 2019
(12.0)