MATHEMATICS AND ORIGAMI

Jesús de la Peña Hernández

Fig. 1 also shows both parabolas with their foci and directrices respectively equidistant

from the co-ordinate origin.

18.8.5 A laminar CUBE.

I give this name to a cube made out of sheets, and determined by its center and

sides respectively: in consequence it is only materialised by the center, vertices, sides

and diagonals. The sheets form some pyramids alike to those studied in Point 18.2.2.1:

they are leant against to each other.

In that Point we saw how the length of the pyramid lateral side was

2

3

. Now

it ́s clear that the double of that side is equal to the cube ́s diagonal 12 + 12 + 12 = 3

18.8.6 Diophantine CUBES

The Greek mathematician Diophantus will give us back up for teamwork with

paperfolding.

The question is this: How to find 4 cubes whose sides will be represented by 4

consecutive natural numbers in such a manner that the greater cube will have a volume

equal to the sum of the other three.

O

F ́

F

d

d ́

1

l

4

2

l

2

3

l

Y

X

x

y

2

2

= ly

= 2lx