Calabi's triangle is the unique triangle other that the equilateral triangle for which the largest
inscribed square can be inscribed in three different ways
(Calabi 1997). Calabi's triangle is an isosceles
triangle with base-to-side length ratio (OEIS A046095),
where
Calabi, E. "Outline of Proof Regarding Squares Wedged in Triangle." Nov. 3, 1997. http://algo.inria.fr/csolve/calabi.html.Conway,
J. H. and Guy, R. K. "Calabi's Triangle." In The
Book of Numbers. New York: Springer-Verlag, p. 206, 1996.Sloane,
N. J. A. Sequences A046095 and A046096 in "The On-Line Encyclopedia of Integer
Sequences."