Trilinears A/a : B/b : C/c
Barycentrics A : B : C
This point is obtained as a limit of perspectors. Let r denote a real number, but not 0 or 1. Using vertex B as a pivot, swing line BC toward vertex A through angle rB and swing line BC about C through angle rC. Let A(r) be the point in which the two swung lines meet. Obtain B(r) and C(r) cyclically. Triangle A(r)B(r)C(r) is the r-Hofstadter triangle; its perspector with ABC is the point given by trilinears
sin(r(A))/sin(A - r(A)) : sin(r(B))/sin(B - r(B)) : sin(r(C))/sin(C - r(C)).
The limit of this point as r approaches 0 is X(360). The two Hofstadter points, X(359) and X(360) are examples of transcendental triangle centers, since they have no trilinear or barycentric representation using only algebraic functions of a,b,c (or sin A, sin B, sin C).
Clark Kimberling, "Hofstadter points," Nieuw Archief voor Wiskunde 12 (1994) 109-114.
X(360) = isogonal conjugate of X(359)
X(360) = anticomplement of X(1115)
, select the center name from the list and, then, click on the vertices A, B and C successively.