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Michael Stifel's 4 X 4 multiplication magic square read by rows.
0

%I #18 Nov 25 2013 02:59:12

%S 32768,4,2,4096,256,32,64,2048,16,512,1024,128,8,16384,8192,1

%N Michael Stifel's 4 X 4 multiplication magic square read by rows.

%C The square formed of natural numbers such that the products of the numbers of each row, each column and each diagonal are the same.

%D Jacques Sesiano, Les carrés magiques dans les pays islamiques, Lausanne: Presses polytechniques et universitaire romandes, 2004, p. 182.

%D Michael Stifel and Philipp Melanchton, Arithmetica integra, Nuremberg: Johannes Petreius, 1544, (29).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MultiplicationMagicSquare.html">Multiplication Magic Square</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Michael_Stifel">Michael Stifel</a>

%H <a href="/index/Mag#magic">Index entries for sequences related to magic squares</a>

%e The multiplication magic square is:

%e |-----|-----|-----|-----|

%e |32768| 4 | 2 | 4096|

%e | | | | |

%e |-----|-----|-----|-----|

%e | 256 | 32 | 64 | 2048|

%e | | | | |

%e |-----|-----|-----|-----|

%e | 16 | 512 | 1024| 128 |

%e | | | | |

%e |-----|-----|-----|-----|

%e | 8 |16384| 8192| 1 |

%e | | | | |

%e |-----|-----|-----|-----|

%e From _Philippe Deléham_, Nov 25 2013: (Start)

%e It is :

%e 2^15, 2^2, 2^1, 2^12

%e 2^8, 2^5, 2^6, 2^11

%e 2^4, 2^9, 2^10, 2^7

%e 2^3, 2^14, 2^13, 2^0, and the square:

%e |----|----|----|----|

%e | 15 | 2 | 1 | 12 |

%e | | | | |

%e |----|----|----|----|

%e | 8 | 5 | 6 | 11 |

%e | | | | |

%e |----|----|----|----|

%e | 4 | 9 | 10 | 7 |

%e | | | | |

%e |----|----|----|----|

%e | 3 | 14 | 13 | 0 |

%e | | | | |

%e |----|----|----|----|

%e is a magic square with constant = 30. (End)

%K nonn,fini,full,tabf

%O 1,1

%A _Arkadiusz Wesolowski_, Nov 23 2013