WOLFRAM|DEMONSTRATIONS PROJECT

Ellipse by Paper Folding

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A
B
C
D
G
H
show lines:
line AB
line AC
line BG
show axes
show ellipse
show creases
save creases
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Let
G
be the center of a circle with radius
r
and let
A
be a point inside the circle. Choose a point
B
on the circumference. Let
C
be the intersection of the perpendicular bisector of
AB
and line
GB
. Then
AC+CG=BG=r
. So the point
C
is on the ellipse with foci
A
and
G
and the sum of the distances from
C
to the foci is
r
.
To construct a tangent on the ellipse, fold the circle so that the circumference touches the point
A
.