The Simplicial Helix and the Equation tan n θ = n tan θ
1985; Cambridge University Press; Volume: 28; Issue: 4 Linguagem: Inglês
10.4153/cmb-1985-045-5
ISSN1496-4287
Autores Tópico(s)Mathematics and Applications
ResumoAbstract Buckminster Fuller has coined the name tetrahelix for a column of regular tetrahedra, each sharing two faces with neighbours, one 'below' and one 'above' [A. H. Boerdijk, Philips Research Reports 7 (1952), p. 309]. Such a column could well be employed in architecture, because it is both strong and attractive. The ( n — 1)-dimensional analogue is based on a skew polygon such that every n consecutive vertices belong to a regular simplex. The generalized twist which shifts this polygon one step along itself is found to have the characteristic equation (λ - 1) 2 {( n - 1)λ n -2 + 2( n - 2)λ n -3 + 3( n - 3)λ n -4 + . . . + ( n - 2)2λ + ( n - 1)} = 0, which can be derived from tan n θ = n tan θ by setting λ = exp (2θ i ).
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