For a nonzero real number and a triangle , swing line segment about the vertex towards vertex through an angle . Call the line along the rotated segment . Construct a second line by rotating line segment about vertex through an angle . Now denote the point of intersection of and by . Similarly, construct and . The triangle having these points as vertices is called the Hofstadter -triangle (Kimberling 1994; 1998, pp. 176-178 and 241-242). For , the resulting triangle is the first Morley triangle.
Kimberling (1994) showed that the Hofstadter triangle is perspective to , and calls perspective center the Hofstadter point.