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Tomás plans a lizard from one square

Tomás, 16 — designing his first origami model from scratch for a school maths fair, with one square of paper and no cuts

The idea in play: every flap needs a circle of paper as wide as the flap is long, so a design is a packing of circles into the square — and corners are the cheapest place.

Tomás wants a lizard with four legs of equal length. His first try folds into a stubby shape: the legs come out half as long as he hoped.

He reads that each flap claims a circle of the square, centred where the flap's tip will come from. His first try put the legs in a small square near the middle of the paper.

Circles in the middle use their whole area. A circle centred at a corner only needs a quarter of its area from the paper — the rest hangs off the edge, which costs nothing.

At the fair, Tomás shows the square with four quarter-circles drawn at its corners before he shows the lizard. The circles are the design; the folding comes after.

Pack the circles yourself →