Click on the figure bellow to exhibit 3D interactive schemes of tetrahedral kites with 1, 4, 16, 64 and 256 tetrahedron cells, respectively. Na janela que se abrirá, para ampliar ou reduzir o esquema, mantenha o botão direito do mouse pressionado e, então, arraste-o.

In the photo of Figure 2, in addition to Alexander Graham Bell, also appears his wife Mabel Gardiner Hubbard. Figure 3 is a reproduction of one of the pages of the tetrahedron kite patent made by Alexander Graham Bell (click on Figure 3 to enlarge it).

Figure 1

Figure 2

Figure 3

The argument given by Simon Newcomb for the impossibility of building large flying machines is a rereading of the Principle of Similitude given by Galileu Galilei in his piece Discorsi e Dimostrazioni Mathematische from 1638. According to this principle, if a biological organism increases its size, it will have to change its own structure. CConsider, for example, the situation of two similar animals, where one of them is twice the scale of the other. The bone “thickness” of the bigger animal wil be 4 times larger than the “thickness” of the corresponding bone of the smaller one, but this bone will tolerate a weight 8 times higher. Therefore, the bone structure of the larger animal will be much more fragile when compared to that of the smaller animal. By Principle of Similitude, a “bigger version” of the small animal will prefer to change its structure (for example, increasing more than 4 times the bone “thickness”) to insure some robustness. It is for this reason that those giant spiders from horros movies, can't exist. The poster of the movie “Tarantula!” is available here.

The following section was extracted from the novel “Gulliver's Travels” written by Jonathan Swift (1667-1745):

The calculation of the volume made by the Lilliputian mathematicians is correct: if Gulliver is 12 times taller than a Lilliputian, so his volume is 123 = 1728 times greater (assuming that Gulliver and the Lilliputians are similar). However, if the metabolism of Lilliputians is equal to Gulliver's metabolism, it is not correct to state that, for having a volume 1728 times greater, Gulliver has to receive 1728 times more food than a Lilliputian would receive. The energy supplied by food is mostly transformed into heat and the rate of heat loss is proportional to the surface area of the body and not to its volume. Note that the surface area of the body of a Lilliputian is 144 times smaller than the surface area of Gulliver's body, whereas the heat generated by his body is 1728 times smaller. So either the body temperature of a Lilliputian is much smaller (he would not have warm blood) or he would have to eat more (in comparison to its size) to generate more energy (like a mouse that is constantly nibbling).

     
Illustrations from the novel “Gulliver's Travels” by Jonathan Swift no Project Gutenberg.