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A232393
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Michael Stifel's 4 X 4 multiplication magic square read by rows.
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0
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32768, 4, 2, 4096, 256, 32, 64, 2048, 16, 512, 1024, 128, 8, 16384, 8192, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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The square formed of natural numbers such that the products of the numbers of each row, each column and each diagonal are the same.
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REFERENCES
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Jacques Sesiano, Les carrés magiques dans les pays islamiques, Lausanne: Presses polytechniques et universitaire romandes, 2004, p. 182.
Michael Stifel and Philipp Melanchton, Arithmetica integra, Nuremberg: Johannes Petreius, 1544, (29).
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LINKS
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EXAMPLE
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The multiplication magic square is:
|-----|-----|-----|-----|
|32768| 4 | 2 | 4096|
| | | | |
|-----|-----|-----|-----|
| 256 | 32 | 64 | 2048|
| | | | |
|-----|-----|-----|-----|
| 16 | 512 | 1024| 128 |
| | | | |
|-----|-----|-----|-----|
| 8 |16384| 8192| 1 |
| | | | |
|-----|-----|-----|-----|
It is :
2^15, 2^2, 2^1, 2^12
2^8, 2^5, 2^6, 2^11
2^4, 2^9, 2^10, 2^7
2^3, 2^14, 2^13, 2^0, and the square:
|----|----|----|----|
| 15 | 2 | 1 | 12 |
| | | | |
|----|----|----|----|
| 8 | 5 | 6 | 11 |
| | | | |
|----|----|----|----|
| 4 | 9 | 10 | 7 |
| | | | |
|----|----|----|----|
| 3 | 14 | 13 | 0 |
| | | | |
|----|----|----|----|
is a magic square with constant = 30. (End)
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CROSSREFS
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KEYWORD
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nonn,fini,full,tabf
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AUTHOR
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STATUS
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approved
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