Let
![K](/media/m/e/1/e/e1ed1943d69f4d6a840e99c7bd199930.png)
and
![K'](/media/m/1/0/f/10ffa5364800c226c075f981c8476000.png)
be two squares in the same plane, their sides of equal length. Is it possible to decompose
![K](/media/m/e/1/e/e1ed1943d69f4d6a840e99c7bd199930.png)
into a finite number of triangles
![T_1, T_2, \cdots , T_p](/media/m/6/1/8/61853cec7f59d728fd66f618ccc23200.png)
with mutually disjoint interiors and find translations
![t_1, t_2,\cdots , t_p](/media/m/9/a/6/9a67acbd8b3ab788e066f93298e4dc4c.png)
such that
%V0
Let $K$ and $K'$ be two squares in the same plane, their sides of equal length. Is it possible to decompose $K$ into a finite number of triangles $T_1, T_2, \cdots , T_p$ with mutually disjoint interiors and find translations $t_1, t_2,\cdots , t_p$ such that
$$K'=\bigcup_{i=1}^{p} t_i(T_i) \ ?$$