Etakaksoisneliö

Etakaksoisneliö is a term used in some Finnish mathematics education and thought experiments to describe a hypothetical geometric figure formed by combining two simple squares. In practice, the term does not correspond to a single standardized object in the formal mathematical literature, and its precise definition can vary between authors or classroom activities. The concept is typically employed to explore ideas about symmetry, composition, and tiling.

One common construction described in didactic contexts places two congruent squares with the same center but rotated relative to each other, often by 45 degrees. The resulting figure is a single, symmetric polygon whose boundary alternates between edges belonging to the two squares. Depending on how the squares are oriented or offset, the shape can appear with different numbers of salient boundary segments and varying degrees of concavity, serving as a concrete example of how simple shapes can combine into more complex forms. Variants might adjust rotation angle, translation, or overlap, producing a family of related figures.

Key properties discussed in educational settings include symmetry (typically dihedral symmetry), decomposability into two squares, and basic area and perimeter relationships derived from the contributing squares and their overlap. The Etakaksoisneliö is mainly used as a pedagogical tool to illustrate concepts such as superposition, boundary construction, and tiling patterns.

History and usage are largely confined to didactic material and classroom exercises in Finland; there is no single authoritative definition. See also: square tiling, polyomino, composite polygon.