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

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%I A291713 #13 Sep 16 2017 15:00:10
%S A291713 36,48,54,64,72,81,96,108,144
%N A291713 144 * preferred ratios of room width / length in Alberti's Ten Books on Architecture.
%C A291713 Coincides with A114334(14) ... A114334(22) (Divisors of 6^6).
%H A291713 Radislav Zuk, <a href="https://doi.org/10.1007/978-3-319-00137-1_38">From Renaissance Musical Proportions to Polytonality in Twentieth Century Architecture</a>, 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
%e A291713 The following table is provided in the Zuk article:
%e A291713 .
%e A291713 Table 38.9 Proportions derived from Alberti's preferred ratios
%e A291713   Plan  Length      Mean              L : H : W
%e A291713   ratio      Width             Height
%e A291713    1:1    1    1    Any mean     1    1 : 1 : 1
%e A291713    3:2    6    4    Arithmetic   5    6 : 5 : 4
%e A291713    3:2   15   10    Harmonic    12   15 :12 :10
%e A291713    4:3    8    6    Arithmetic   7    8 : 7 : 6
%e A291713    2:1    4    2    Arithmetic   3    4 : 3 : 2
%e A291713    9:4    9    4    Geometric    6    9 : 6 : 4
%e A291713   16:9   16    9    Geometric   12   16 :12 : 9
%e A291713    3:1    3    1    Arithmetic   2    3 : 2 : 1
%e A291713    8:3    8    3    Fibonacci    5    8 : 5 : 3
%e A291713    4:1    4    1    Geometric    2    4 : 2 : 1
%e A291713 .
%e A291713 a(8)=108 is in the sequence, because the ratio 144/108 corresponds to the plan ratio of 4:3.
%Y A291713 Cf. A114334, A291714, A291715, A291719.
%K A291713 nonn,fini,full
%O A291713 1,1
%A A291713 _Hugo Pfoertner_, Aug 30 2017