Fold a piece of paper in half. Cut a shape out of the folded edge. Open it up — the result is symmetric about the fold line. Reflection symmetry, made physical.
You fold a square sheet in half twice (the second fold perpendicular to the first), cut a shape from the corner, and unfold. How many lines of symmetry does the cut-out pattern have?
Folds → symmetry
- 1 fold → one mirror line (a simple heart or butterfly).
- 2 folds (perpendicular) → 4 mirror lines.
- 3 folds → 6-fold, snowflake-like.
- Each cut you make is copied to every mirrored position at once.
Why can't you cut a shape with exactly 3 lines of reflection symmetry from a sheet folded only along straight folds through one point?
Curvy cuts work too: a wavy slice on the fold unfolds into a perfectly symmetric blob you could never draw freehand.
Try this
Fold once for one line of symmetry. Fold twice (perpendicular) for two lines of symmetry — you'll get something with four-fold reflection. Fold three or four times for snowflake-like shapes.
Curvy cuts make stranger results. Try cutting a wavy line, then unfolding — you'll get a perfectly symmetric blob you couldn't have drawn freehand.