MATHEMATICS AND ORIGAMI

Mathematics and Origami

To prove it we must consider the ellipse ́s peculiar equation that relates the radius vec-

tors and the Cartesian co-ordinates of one point on it, with its basic parameters:

−cx+a^2 −aρ= 0

From it we can write x a ex

a

c

ρ=a− = −

After (3) it is

e

a

c

a

OC= =

2

, hence:

x

e

a

PE=OC−x= −

And finally we ́ll have:

e

x

e

a

a ex

PE

=

−

−

=

ρ

7

A ́ O

d

A C X

B

B ́

F ́ F

Y

P(x,y)

E

Interlude

✂