Jesús de la Peña Hernández

2 2

4 5

(^180) , 0329422 36 230 ,^19922 /^23.^020 /
98 2 , 3677979 10
E = Kg mm = Kg cm
× ×
× ×

−
2 2
4 5
(^280) , 0232925 40 724 ,^20347 /^72.^420 /
134 1 , 6742006 10
E = Kg mm = Kg cm
× ×
× ×

−
Here there are several E values corresponding to different materials to be compared:
MATERIAL E (Kg / cm^2 )
Pine 96.000
Holm oak 108.000
Beech 180.000
Lead 50.000
Glass 700.000
Forged iron 2.000.000
20.2 THE π NUMBER
The construction of a cylinder (Point 19) profiting of paper flexibility will help us to fo-
cus closely on the π number.
Then we saw how, to properly dress the cylinder, it was required to interlock and glue
the lap joints, besides adjusting inside it a cone and a sphere.
The reason was that under those conditions, the cylinder does not yield spontaneously a
circular section because of the discontinuity of paper flexibility in the vicinity of the lap joints.
The best way to lessen that effect is to construct a tube by wrapping up the paper around itself
with as many layers as possible: the greater the number of layers, the higher the cylindrical
(circular) precision.
Fig. 1 shows a tube obtained by rolling a paper three times around itself, plus an arc
AB. Since the circumference length is πd, we should divide that length by its diameter to get π.
The process asks for these precautions:

• Make sure that edge e is properly fixed on the tube ́s outer surface (use glue, an adhesive
  tape, etc.).


• Every layer of paper must seat tight against each other as well as the remains AB over the
  last one.


• To know the paper thickness. For copying paper we take a = 0,11 mm (see Point 20.1).


• To know also the paper ́s initial development. In our case it is A ́B = 297 mm since we start
  with a DIN A4 rectangle.


• To measure the exterior tube diameter with the greatest possible accuracy. We know how
  difficult it is to reach a certain precision because of the inherent cylindrical inaccuracy asso-
  ciated to a reduced number of layers, and also due to the scarce resolution of a measuring

e

i B

A ́

A

1