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A291713
144 * preferred ratios of room width / length in Alberti's Ten Books on Architecture.
3
36, 48, 54, 64, 72, 81, 96, 108, 144
OFFSET
1,1
COMMENTS
Coincides with A114334(14) ... A114334(22) (Divisors of 6^6).
LINKS
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
KEYWORD
nonn,fini,full
AUTHOR
Hugo Pfoertner, Aug 30 2017
STATUS
approved