  If we label the vertices of a triangle with 1, 2 and 4, and the orthocentre
with 7, then any of the four numbers 1, 2, 4, 7 is the nim-sum of the other
three and is their orthocentre. Regard the triangle as an orthocentric
quadrangle. Steiner's theorem states that the reflexions of a point on a
circumcircle in each of the three edges of the corresponding triangle are
collinear and collinear with its orthontre. This line intersects the
circumcircles in new points to which the theorem may be applied. Iteration of
this process with the triangle and the points rational leads to a "trisequence"
whose properties merit study.
