For a nonzero real number r and a triangle Δ A B C, swing line segment B C about the vertex B towards vertex A through an angle r B. Call the line along the rotated segment L. Construct a second line L' by rotating line segment B C about vertex C through an angle r C. Now denote the point of intersection of L and L' by A(r). Similarly, construct B(r) and C(r). The triangle having these points as vertices is called the Hofstadter r-triangle (Kimberling 1994; 1998, pp. 176-178 and 241-242). For r = 1/3, the resulting triangle is the first Morley triangle. Kimberling showed that the Hofstadter triangle is perspective to Δ A B C, and calls perspective center the Hofstadter point.

first Morley triangle | Hofstadter point