  A circular word, or a necklace, is an equivalence class under conjugation of
a word. A fundamental question concerning regularities in standard words is
bounding the number of distinct squares in a word of length $n$. The famous
conjecture attributed to Fraenkel and Simpson is that there are at most $n$
such distinct squares, yet the best known upper bound is $1.84n$ by Deza et al.
[Discr. Appl. Math. 180, 52-69 (2015)]. We consider a natural generalization of
this question to circular words: how many distinct squares can there be in all
cyclic rotations of a word of length $n$? We prove an upper bound of $3.14n$.
This is complemented with an infinite family of words implying a lower bound of
$1.25n$.
