Cut a Shape Into Smaller Copies of Itself
Some shapes have a strange property: you can slice them into several smaller pieces, and every single piece is a smaller copy of the original shape. An L-shaped tromino, for instance, can be cut into four smaller L-trominoes with no gaps or overlaps. Can you find the cut — and can you picture a shape where this trick simply doesn't work?
Reveal the answer
The L-tromino divides cleanly into 4 smaller L-trominoes (each scaled by 1/2), making it a 'rep-4' shape; combine copies and you also get rep-9, rep-16 and so on. Recreational mathematician Solomon Golomb coined the term 'rep-tile' (a pun on reptile) for any shape with this property, and Martin Gardner popularized them in his Scientific American 'Mathematical Games' column, May 1963.