Constructions with Paper Folding

A
B
C
D
G
H

show creases

save creases

delete creases

save mapped points:

A'

B'

C'

D'

G'

H'

delete mapped points

special cases (set initial settings first)

Messner's

3

2

Abe's angle trisection

parabola

You can fold the unit square piece of paper, yellow on one side, light blue on the other, by dragging its lower-left corner. Use the 2D sliders to place the points

A

,

B

, … on the paper. There are three special cases:

• Messner's method for doubling a cube using origami

• Abe's angle trisection

• Constructing a point on a parabola given by a horizontal directrix and focus

A

. Suppose the point

B

is on the directrix; find a crease that maps

B

into

A

. Then the intersection of the crease with the vertical line through

B

is on the parabola.