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Melencolia

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by Dr. Hans-Christian Solka
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Melencolia by Dr. Hans-Christian Solka

The date 1514 A.D. actually means something to you? It's possible to instantly construct that kind of magic square on the backside of a business card and hand it out as giveaway. I love the method because of its simplicity. Even better: once learned the method is impossible to forget!

  • Works with any magic sum greater 33 or with the century and year numbers of any named year.
  • The magic square is balanced.
  • The numbers are in sequence. There are no duplicate numbers.
  • The magic sum can be obtained in up to 68 different ways.
  • Extremely simple calculations and memory work.
Table of Contents:
  1. Introduction
  2. Part I - The construction of Duerer's magic square
    1. The first pass: great summit
    2. The second pass: little valley
    3. The third pass: little summit
    4. The fourth pass: great valley
    5. The completed magic square
    6. The handling of a different initial number
    7. The complementary pair sum
    8. Square and cube sums
  3. The summation patterns of Duerer's type magic squares
    1. Even magic sums
    2. Odd magic sums
    3. Standard position
    4. Transformation properties of associated magic squares
  4. The zigzag principle for semi-magic squares
    1. The first zigzag pass
    2. The second zigzag pass
    3. The third zigzag pass
    4. The fourth zigzag pass
    5. The completed semi-magic square
  5. The foursome magic square
    1. The first pass: great summit
    2. The second pass: little valley
    3. The third pass: little summit
    4. The fourth pass: great valley
    5. The completed foursome magic square
    6. The handling of an even total
  6. The instant foursome magic square
    1. The basic instant magic square
    2. The "blitz I"
    3. The "blitz II"
  7. The balanced foursome magic square
    1. The balanced magic square; without a remainder
    2. The balanced magic square; remainder of two
    3. The balanced magic square; remainder of one
    4. The balanced magic square; remainder of three
  8. Part II - The modified Duerer's magic square
    1. Original and modified Dürer's magic square
    2. The cloth hanger transformation
    3. The foursome attribute
  9. The summation patterns of modified Duerer's type magic squares
    1. Even magic sums
    2. Odd magic sums
    3. The flow of the summit and valley pattern
  10. The handling of magic sums greater than 34
    1. An even magic sum; without a remainder
      1. The first pass: great summit
      2. The second pass: little summit
      3. The third pass: little valley
      4. The fourth pass: great valley
      5. The completed magic square
      6. A simple forcing matrix to avoid calculations
    2. An even magic sum; remainder of two
      1. The first pass: great summit
      2. The second pass: little summit
      3. The third pass: little valley
      4. The fourth pass: great valley
      5. The completed and transformed magic squares
    3. An odd magic sum; remainder of one
      1. The first pass: great summit
      2. The second pass: little summit
      3. The third pass: little valley
      4. The fourth pass: great valley
      5. The completed and transformed magic squares
    4. An odd magic sum; remainder of three
      1. The first pass: great summit
      2. The second pass: little summit
      3. The third pass: little valley
      4. The fourth pass: great valley
      5. The completed and transformed magic squares
  11. Part III - Ideas for routines
    1. Spectator's height
    2. Any number in any cell
    3. Spectator's year of birth
    4. Counting backwards
    5. Counting a sequence of only odd or even numbers
    6. The lightning magic year square
    7. Annemann-like presentation of the magic year square

3rd edition 2018, 68 pages
word count: 1775 which is equivalent to 7 standard pages of text

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07/18/2018
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