MATHEMATICS AND ORIGAMI

Jesús de la Peña Hernández

1.2. OBTENTION OF STRAIGHT LINES (valley, mountain)

1.2.1. THROUGH ONE POINT: infinity, a)

1.2.2. THROUGH TWO POINTS: just one, b)

1.2.3. SYMMETRICAL TO THE EDGE a THROUGH POINT P: The folding line

is the axis of symmetry. There is an infinity of solutions: a paper edge can be

folded over one inner point, in many ways.

1.2.4. FOLDING OF A PAPER CORNER E over the edge a.

As can be seen, there is an infinity of solutions: The envelope of all those folding

lines is a parabola so defined: focus E; axis EB; directrix a; vertex V. Therefore, for

point P on the parabola, we have PA = PE.

1.2.5 FOLDING OF ONE EDGE OVER AN INTERNAL POINT.

Same approach as in Point 1.2.4:

a) b)

a a

P P

A

V

a B a

E

B

P E