Category:Sam Loyd's Missing Square

This category contains pages concerning Sam Loyd's Missing Square:

Consider a square of side length $13$.

Let it be divided into:

a $13 \times 5$ rectangle, divided into two right triangles by its diagonal

a $13 \times 8$ rectangle, divided into trapezia with side lengths $8$ and $5$:

Let the pieces be rearranged to form two long right triangles arranged to form a $21 \times 8$ rectangle.

The area of the square is $13 \times 13 = 169$.

The area of the rectangle is $21 \times 8 = 168$.

Where did the missing $1 \times 1$ square go?

Source of Name

This entry was named for Samuel Loyd.