Number PatternsAreaMedium
The Vanishing Area
Cut a square, rebuild it as a rectangle — and one unit of area mysteriously vanishes.
Worked demonstration
A square of side 3 (area 9 square units) is cut into four pieces and slid together into a 2-by-5 rectangle. Measure the rectangle: what is its area in square units?
Try it yourself
Why it works
The pieces don't quite meet along the diagonal: consecutive Fibonacci numbers satisfy F(n-1)·F(n+1) − F(n)² = ±1, hiding one unit.
Background & Explore Further
This is the classic 'missing square' puzzle (Curry's paradox), exploiting how close Fibonacci ratios sit. Explore Cassini's identity and why 'looks straight' isn't 'is straight'.
Maths Made Magic — Queen Mary University of London (cs4fn)