Problem list（9 problems）
- How many degrees is angle x? Every folding problem runs on two facts: overlapping angles are equal, and the strip's parallel edges give equal alternate angles
- What is the area of the folded-over triangle? Folding changes none of the area, the lengths or the angles
- How far from the left wall did it bounce? For a bounce, reflect and straighten
- Area of the overlap? Spotting "these two match when you rotate" gives you the area without ever knowing the angle
- How many lines of symmetry does it have? Many people count only the corner-to-corner lines and stop at half the answer
- Through what angle must it turn to match itself again? The turn that brings a shape back onto itself is "a full turn ÷ the number of corners"
- How big is angle AED? Whenever a square meets an equilateral triangle, start from the 30° left over between 90° and 60°
- How many degrees is the gap angle x? Equilateral triangles, squares and regular hexagons tile the plane; regular pentagons cannot — 108° does not divide 360° exactly
- Area of the inner quadrilateral? However lopsided the original quadrilateral, joining the midpoints always gives a parallelogram, and its area is always half
Other ideas
- Shearing — moving a shape without changing its area
- Ratios — answers without fixing a single number
- Add, then subtract — an overlap is a counting problem
- Circles and sectors — multiply by π once, at the very end
- Chasing angles — there are only four tools
- Decide how to count, then count
- Flatten the solid before you think about it
- Write the same thing two different ways
- Back to why the formula works