The Squares That Swap

one gap becomes two, and the shaded area never blinks.

slide four triangles until the tilted gap splits in two

Four identical right triangles fit the same square frame two different ways — pinwheeled around one tilted gap, or slid into the corners, leaving two smaller square gaps side by side. The leftover area is counted honestly from the frame and the triangles the whole time and never changes, which is a² + b² = c², felt as a slide of four triangles rather than read as an equation.

Concepts: geometry, area.

An interactive you play with one thumb, on Wundr.