14.7.4  Equilateral triangles in space: equilateral_triangle

See Section 13.8.4 for equilateral triangles in the plane.

The equilateral_triangle command returns and draws equilateral triangles.

• equilateral_triangle takes three mandatory arguments and one optional argument:
  • A,B,P, three points.
  • Optionally, var, a variable name.
• equilateral_triangle(A,B,P ⟨,var⟩) returns and draws equilateral triangle ABC, where C and P are on the same side of line AB in plane ABP.
  If the argument var is given, it will be assigned the value of C.

Examples.

• Input:

  A:= point(0,0,0);

  B:= point(3,3,3);

  P:= point(0,0,3)

  equilateral_triangle(A,B,P)

  Output:
  
• Input:

  A:= point(0,0,0);

  B:= point(3,3,3);

  P:= point(0,0,3)

  equilateral_triangle(A,B,P,C)

  simplify(coordinates(C))

  Output:

  ⎡ ⎢ ⎢ ⎣

  −3  √ 6 +6 4

  ,

  −3  √ 6 +6 4

  ,

  3  √ 6 +3 2

  ⎤ ⎥ ⎥ ⎦