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A291719 Numbers occurring in Ezra Ehrenkrantz's "Modular Coordination System".

%I A291719 #14 Aug 30 2017 21:38:12
%S A291719 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 A291719 72,80,90,96,108,120,128,144,180,192,216,240,288,360,384,432,576,720,
%U A291719 1152
%N A291719 Numbers occurring in Ezra Ehrenkrantz's "Modular Coordination System".
%C A291719 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 A291719 Ezra Ehrenkrantz, Modular Number Pattern, Tiranti, London 1956.
%H A291719 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 A291719 Numbers of the form Fibonacci(i+2)*2^j*3^k; i, j=0..4, k=0..2.
%e A291719 The number pattern in three dimensions:
%e A291719                      A    B     C     D     E
%e A291719           Plate 3 +---+-----+-----+-----+-----+
%e A291719                  /|  9   18    36    72   144 |
%e A291719                 / | 18   36    72   144   288 |
%e A291719                /  | 27   54   108   216   432 |
%e A291719               /   | 45   90   180   360   720 |
%e A291719              /    | 72  144   288   576  1152 |
%e A291719             /     +---+-----+-----+-----+-----+
%e A291719            / A    B     C     D     E        /
%e A291719   Plate 2 /---+-----+-----+-----+-----+     /
%e A291719          /|  3    6    12    24    48 |    /
%e A291719         / |  6   12    24    48    96 |   /
%e A291719        /  |  9   18    36    72   144 |  /
%e A291719       /   | 15   30    60   120   240 | /
%e A291719      /    | 24   48    96   192   384 |/
%e A291719     /     +---+-----+-----+-----+-----/
%e A291719    /  A    B     C     D     E       /
%e A291719   +---+-----+-----+-----+-----+ Plate 1
%e A291719   |  1    2     4     8    16 |    /
%e A291719   |  2    4     8    16    32 |   /
%e A291719   |  3    6    12    24    48 |  /
%e A291719   |  5   10    20    40    80 | /
%e A291719   |  8   16    32    64   128 |/
%e A291719   +---+-----+-----+-----+-----+
%p A291719 with(combinat):
%p A291719 {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 A291719 Cf. A000045, A051037.
%K A291719 nonn,fini,full
%O A291719 1,2
%A A291719 _Hugo Pfoertner_, Aug 30 2017