MATHEMATICS AND ORIGAMI

Jesús de la Peña Hernández

In this figure we may observe:

• Points D, C have been obtained by calculus (Point 7.11).


• From focuses D, C three radiating lines are cast, respectively, toward axes OX and OY.


• Each two of these three lines are parallel (perpendicular to the same tangent). The tangent of
  the angle formed by one of the rays and OX is the solution of the equation: obviously there
  are three of them.


• The three folding lines resulting from the simultaneous fold of D over OX and C over OY are
  the common tangents to these two parabolas: focus D (and directrix OX) and focus C (and
  directrix OY).


• The axes of those parabolas are, of course, the perpendiculars to the directrices from the fo-
  cuses.

Interlude

D

C

O

X

2