MathDB

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, \ldots, T_p

with mutually disjoint interiors and find translations

t_1, t_2, \ldots, t_p

such that

K'=\bigcup_{i=1}^{p} t_i(T_i) \ ?

Problem Statement