All Questions

Definition: A partition of a planar figure into finitely many pieces that are all similar to itself and also mutually non-congruent may be called a self-similar perfect partition. A classical example ...

A perfect squaring of a rectangle may be defined as a partition of the rectangle into finitely many squares all of which are mutually non-congruent. https://en.wikipedia.org/wiki/Squaring_the_square ...

Ref: https://en.wikipedia.org/wiki/Squaring_the_square A perfect cubing of a cube is a partition of the cube into some finite number of smaller cubes that are pair-wise non-congruent. The above page ...

For which positive integers n is $n^2$ the sum of precisely n smaller positive squares? Of these n x n squares, which can be actually cut into n smaller squares?

Is it possible to completely tile a square with different rectangles of integer sides but all with the same area? The original problem, not requiring integer sides for rectangles, was proposed by Joe ...

Is it possible to construct a squared square out of consecutive integer squares? Be it 1,2,3,...n or k,k+1,k+2,...n.