13.17.5  Pole and polar: pole polar

Given a circle centered at O, a point A is a pole and a line L is the corresponding polar if L is the line passing through the inversion of A with respect to the circle (see Section 13.15.7) passing through the line OA.

The polar command finds the polar of a point.

• polar takes two arguments:
  • C, a circle.
  • A, a point.
• polar(C,A) returns and draws the polar of the point A with respect to C.

Example.
Input:

Output:

The pole command finds the pole of a line.

• pole takes two arguments:
  • C, a circle.
  • L, a line
• pole(C,L) returns and draws the pole of the line L with respect to C.

Examples.

• Input:
  pole(circle(0,1),line(i,1))
  Output:
  
• Input:
  affix(pole(circle(0,1),line(i,1)))
  Output:

  1+i