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Paper folding

For the grown-up beside a child who loves paper folding.

The child's own door is Paper folding on Spark & Anvil.

There is no Whetstone tool or course for paper folding yet, so this page is the sideline card and your child's ladder.

The sideline card

Three numbers to notice

  1. Fold a square in half, edge to edge: each half is half the square, and the crease is a line of symmetry.
  2. Fold it corner to corner instead and the crease cuts the two corners it runs through into 45° angles.
  3. Folders have shown there are exactly seven ways one fold can line up points and creases, and a fold can split an angle into three, which a ruler and compass cannot.

On the way home, ask: “Which fold was the trickiest to line up?”

Ask because you are curious, and let any answer stand. Print this page for a half-page card.

Numbers checked against: Robert J. Lang: the Huzita–Justin axioms; worked by hand, lines 1 and 2 (half of a square; a diagonal halves a right angle)

Your child's ladder · on Spark & Anvil

The same idea at every age

  1. Ages 3–5Fold together
  2. Ages 6–8Half of a half
  3. Ages 9–14Seven folds? and 1 more
  4. Ages 15–18One crossing and 1 more

Your child will meet this idea again at every age. The sideline card is the part for you.