The one Triangle in addition to the Equilateral Triangle for which the largest inscribed Square
can be inscribed in three different ways. The ratio of the sides to that of the base is given by
(Sloane's A046095), where

is the largest Positive Root of

which has Continued Fraction [1, 1, 1, 4, 2, 1, 2, 1, 5, 2, 1, 3, 1, 1, 390, ...] (Sloane's A046096).

**References**

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. A046095 and A046096 in ``An On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html.

© 1996-9

1999-05-26