A4 Paper Folding
Author: Peter Fox
Date: 11/09/2006

Take a sheet of A4 paper and fold the top left corner so that it touches somewhere along the opposite (long) side.

Explore the relationship between the placement of the fold along the short side and the area of the small triangle formed in the bottom left corner.

When is this area greatest?

Drag the point P to explore different positions of the fold.

Call OP "x" and try to build an algebraic function which models this relationship.

Double click to bring up a full application window, and enter your function to test it against the geometric model shown here.

Is there a "best" fold position for any size paper?

Drag Me!

Position of fold (OP) =

Area of triangle OPE =

Fold a piece of A4 paper as shown.
(NOTE that A4 paper is 29.7 x 21 cm)

Explore the relationship between the
position of the fold (OP) and the area
of the triangle OPE formed?

When is this area greatest?

O = (30, 10)
A = (30, 31)
C = (59, 10)
B = (59, 31)
P_1, o, b, c, a = Polygon(O, C, B, A)
P = Point(a)
d = Circle(P, A)
E = Intersect(d, o)
e = Segment(P, E)
f = Vector(A, E)
g = OrthogonalLine(E, e)
F = Intersect(c, g)
h = OrthogonalLine(P, f)
G = Intersect(h, b)
i = OrthogonalLine(G, h)
H = Intersect(i, g)
Q, d_1, g_1, h_1, e_1 = Polygon(P, G, H, E)
R, e_2, d_2, f_1 = Polygon(P, F, E)
S, e_3, d_3, o_1 = Polygon(P, O, E)
D = (25, 25)
u = Vector(D, P)
j = Segment(O, P)
T4: j + ""
T5: S + ""
W: (j, S)
I = Mirror(P, O)
T, e_4, o_2, i_1 = Polygon(O, I, E)
myarea(x) = 0.0
height(x) = 0.0
hypot(x) = 0.0
base(x) = 0.0
f1(x) = myarea(x)