MATHEMATICS AND ORIGAMI

Mathematics and Origami

19 ROUND BODIES

Strictly speaking they are the cylinder, cone and sphere. We shall construct them by

means of interlocking (fix them with adhesive tape if needed, the cylinder in particular). Just

only a paper flexion is required to get cylinder and cone.

Cylinder and cone bases will be virtual (intersections between each other or with the

plane of reference). The sphere will be in the laminar mode to Donovan A. Johnson ́s design,

hence, virtual (recall Point 18.8.5 as an analogy).

We shall associate the three bodies to form a geometric set. Fig.1 is a section of that set

whose characteristics are based on the fact that the laminar sphere has R as radius.

Here we have those characteristics:

• The sphere rests on the reference plane: it looks like flattened in a value b.


• A well-fit cylinder that in turn rests on the plane of reference too, will cover the
  sphere.


• An inverted cone, whose vertex coincides with the sphere ́s center, is tangent to the
  three trirrectangular circles defining the sphere. Besides, it intercepts the cylinder
  just at its upper base. The cone base is situated at a distance R / 2 over the mentioned
  cylinder ́s upper base.

SPHERE

As said, its radius is R and will consist in three circles also of radius R (Fig. 2).

It is required to perform the cuts and folds as indicated and then to introduce circles b

and c into the a. We must recall that circle b should take a square shape to go into circle

a. Finally undo the foldings and dress the set. Three circles that intersect each other in a

trirrectangular mode define that spherical set.

CYLINDER

Fig. 3 is the cylinder development with the indicated dimensions.

CONE

Idem cylinder (Fig. 4).

R

b

H plane of reference

a

R ́

R 2

1