A291713 144 * preferred ratios of room width / length in Alberti's Ten Books on Architecture.

36, 48, 54, 64, 72, 81, 96, 108, 144

Offset

1,1

Comments

Coincides with A114334(14) ... A114334(22) (Divisors of 6^6).

Links

Table of n, a(n) for n=1..9.

Radislav Zuk, From Renaissance Musical Proportions to Polytonality in Twentieth Century Architecture, Chapter 38 in Volume 1 of K. Williams and M. J. Ostwald (eds.), Architecture and Mathematics from Antiquity to the Future, DOI 10.1007/978-3-319-00137-1_38, Springer International Publishing Switzerland 2015

Example

The following table is provided in the Zuk article:
.
Table 38.9 Proportions derived from Alberti's preferred ratios
  Plan  Length      Mean              L : H : W
  ratio      Width             Height
   1:1    1    1    Any mean     1    1 : 1 : 1
   3:2    6    4    Arithmetic   5    6 : 5 : 4
   3:2   15   10    Harmonic    12   15 :12 :10
   4:3    8    6    Arithmetic   7    8 : 7 : 6
   2:1    4    2    Arithmetic   3    4 : 3 : 2
   9:4    9    4    Geometric    6    9 : 6 : 4
  16:9   16    9    Geometric   12   16 :12 : 9
   3:1    3    1    Arithmetic   2    3 : 2 : 1
   8:3    8    3    Fibonacci    5    8 : 5 : 3
   4:1    4    1    Geometric    2    4 : 2 : 1
.
a(8)=108 is in the sequence, because the ratio 144/108 corresponds to the plan ratio of 4:3.

Crossrefs

Cf. A114334, A291714, A291715, A291719.

Sequence in context: A160063 A260927 A361098 * A370266 A287840 A244326

Adjacent sequences: A291710 A291711 A291712 * A291714 A291715 A291716

Keyword

nonn,fini,full

Author

Hugo Pfoertner, Aug 30 2017

Status

approved