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%I #14 Aug 30 2017 21:38:12
%S 1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,27,30,32,36,40,45,48,54,60,64,
%T 72,80,90,96,108,120,128,144,180,192,216,240,288,360,384,432,576,720,
%U 1152
%N Numbers occurring in Ezra Ehrenkrantz's "Modular Coordination System".
%C Cited from Jay Kapraff’s article: "... architect Ezra Ehrenkrantz created a system of architectural proportion that incorporates aspects of Alberti’s and Palladio’s systems made up of lengths factorable by the primes 2, 3, and 5, along with the additive properties of Fibonacci series."
%D Ezra Ehrenkrantz, Modular Number Pattern, Tiranti, London 1956.
%H Jay Kappraff, <a href="https://link.springer.com/chapter/10.1007/978-3-319-00137-1_37">Musical Proportions at the Basis of Systems of Architectural Proportion both Ancient and Modern</a>, Chapter 37 in Volume I of K. Williams and M.J. Ostwald (eds.), Architecture and Mathematics from Antiquity to the Future, DOI 10.1007/978-3-319-00137-1_37, Springer International Publishing Switzerland 2015
%F Numbers of the form Fibonacci(i+2)*2^j*3^k; i, j=0..4, k=0..2.
%e The number pattern in three dimensions:
%e A B C D E
%e Plate 3 +---+-----+-----+-----+-----+
%e /| 9 18 36 72 144 |
%e / | 18 36 72 144 288 |
%e / | 27 54 108 216 432 |
%e / | 45 90 180 360 720 |
%e / | 72 144 288 576 1152 |
%e / +---+-----+-----+-----+-----+
%e / A B C D E /
%e Plate 2 /---+-----+-----+-----+-----+ /
%e /| 3 6 12 24 48 | /
%e / | 6 12 24 48 96 | /
%e / | 9 18 36 72 144 | /
%e / | 15 30 60 120 240 | /
%e / | 24 48 96 192 384 |/
%e / +---+-----+-----+-----+-----/
%e / A B C D E /
%e +---+-----+-----+-----+-----+ Plate 1
%e | 1 2 4 8 16 | /
%e | 2 4 8 16 32 | /
%e | 3 6 12 24 48 | /
%e | 5 10 20 40 80 | /
%e | 8 16 32 64 128 |/
%e +---+-----+-----+-----+-----+
%p with(combinat):
%p {seq(seq(seq(fibonacci(i+2)*2^j*3^k, k=0..2), j=0..4), i=0..4)}[]; # _Alois P. Heinz_, Aug 30 2017
%Y Cf. A000045, A051037.
%K nonn,fini,full
%O 1,2
%A _Hugo Pfoertner_, Aug 30 2017
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