14.13.9  Checking if an object in space is an equilateral triangle: is_equilateral

See Section 13.16.5 for checking for equilateral triangles in two-dimensional geometry.

The is_equilateral command determines whether or not a geometric object is an equilateral triangle.

• is_equilateral takes one argument:
  G, a geometric object or a sequence of three points assumed to be the vertices of a triangle.
• is_equilateral(G) returns 1 if the object is an equilateral triangle and returns 0 otherwise.

Examples.

• Input:
  is_equilateral([2,0,0],[0,0,0],[1,sqrt(3),0])
  Output:

  1

• Input:

  T:= triangle_equilateral([2,0,0],[0,0,0],[1,sqrt(3),0])

  is_equilateral(T)

  Output:

  1

• Input:
  is_equilateral([2,0,0],[0,2,0],[1,1,0])
  Output:

  0