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A291719
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Numbers occurring in Ezra Ehrenkrantz's "Modular Coordination System".
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4
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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
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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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."
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REFERENCES
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Ezra Ehrenkrantz, Modular Number Pattern, Tiranti, London 1956.
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LINKS
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FORMULA
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Numbers of the form Fibonacci(i+2)*2^j*3^k; i, j=0..4, k=0..2.
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EXAMPLE
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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 |/
+---+-----+-----+-----+-----+
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MAPLE
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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
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CROSSREFS
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KEYWORD
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nonn,fini,full
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AUTHOR
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STATUS
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approved
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