When decomposing a rectangle to form new two-dimensional polygons, which geometric part can NOT be formed?

When decomposing a rectangle into new two-dimensional polygons, the concept involves breaking down the rectangle into shapes that entirely fill the space without any overlaps or gaps. A rectangle can be divided into various polygons like triangles, squares, and congruent rectangles, as these shapes can be created by cutting along straight lines parallel to or intersecting the existing edges of the rectangle.

However, a circle cannot be formed through such decomposition. This is because a circle is a curved shape, and the straight edges of the rectangle do not allow for the creation of a circular area. The nature of a rectangle is defined by its straight edges and corners, making it impossible to derive a shape with curved sides from it. Thus, the formation of a circle is incompatible with the properties of a rectangle during decomposition into polygons, affirming that one circle cannot be formed from a rectangle.