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

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, 72, 80, 90, 96, 108, 120, 128, 144, 180, 192, 216, 240, 288, 360, 384, 432, 576, 720, 1152

Offset: 1

Author

Hugo Pfoertner, Aug 30 2017

Keywords

• nonn
• fini
• full

Comments

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."

Examples

			The number pattern in three dimensions:
                     A    B     C     D     E
          Plate 3 +---+-----+-----+-----+-----+
                 /|  9   18    36    72   144 |
                / | 18   36    72   144   288 |
               /  | 27   54   108   216   432 |
              /   | 45   90   180   360   720 |
             /    | 72  144   288   576  1152 |
            /     +---+-----+-----+-----+-----+
           / A    B     C     D     E        /
  Plate 2 /---+-----+-----+-----+-----+     /
         /|  3    6    12    24    48 |    /
        / |  6   12    24    48    96 |   /
       /  |  9   18    36    72   144 |  /
      /   | 15   30    60   120   240 | /
     /    | 24   48    96   192   384 |/
    /     +---+-----+-----+-----+-----/
   /  A    B     C     D     E       /
  +---+-----+-----+-----+-----+ Plate 1
  |  1    2     4     8    16 |    /
  |  2    4     8    16    32 |   /
  |  3    6    12    24    48 |  /
  |  5   10    20    40    80 | /
  |  8   16    32    64   128 |/
  +---+-----+-----+-----+-----+
		

References

• Ezra Ehrenkrantz, Modular Number Pattern, Tiranti, London 1956.

Links

• Jay Kappraff, Musical Proportions at the Basis of Systems of Architectural Proportion both Ancient and Modern, 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

Crossrefs

Cf. A000045, A051037.

Programs

Maple

with(combinat):
{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

Formula

Numbers of the form Fibonacci(i+2)*2^j*3^k; i, j=0..4, k=0..2.