MATHEMATICS AND ORIGAMI

Jesús de la Peña Hernández

Let ́s set the hypothesis that z’ = 0 when its last factor ́s value is 0. As the previous fac-

tor is a square root in a denominator, we ́ll have to check afterwards that this factor ́s value is

not 0 for the x solution.

Therefore it should be

0

2

12

2

1

2

2 2

2

 − =











 + −











−

a

x x x

a

x

a

x under the condition of

2

1

2













x−

a

≠ 0

Simplifying last equation it is easy to see that

x a

4

3

=

which in fact does not nullify either the expressions mentioned above.

Folding O over CD through a point B such that x a

4

3

= we get the minimum segment

AB.

The reader can check it by himself trying successive folds to approximate AB mini-

mum.

Interlude