Friday, April 30, 2010


Here are the two latest winners in Christian Boyer's six enigmas Magic Square Contest

Toshihiro Shirakawa of Japan is the winner of €1,100 for his efforts.


Thursday, April 29, 2010


A retention magic square is a magic square whose larger numbers surround smaller numbers forming retention lakes or ponds. Here is an example:

Finally there has been a change in the standings in Al Zimmerman's Magic Square Contest. As predicted in the April 12 Blog, the Germans are favored to do well in this contest.

The Germans are now one-two with Hermann Jurksch leading and Walter Trump trailing by only 0.004 points. Walter Trump is the favorite to win as he is one of the pioneers of Retention Magic Squares, a brilliant concept of combinatory mathematics.

Lady Gaga likes retention magic squares!!

Thursday, April 22, 2010


Here we can see an order to the prime numbers in the 19x19 Magic Square.

One can see that the numbers at the end of a column or row will continue in numerical sequence at the beginning of the next column or row. Therefore, a magic square in the Luo Shu format will also describe a three dimensional torus.

Notes of interest:

the number 2, the only even prime number stands alone as the only prime number in its row or column

there are 72 prime numbers in the 19x19 Magic Square
there are 71 odd prime numbers in the square, 71 is a prime number

In this 19x19 Magic Square, the prime numbers will line up with one another in the three dimensional torus shape.

The number 19 is the seventh odd prime number and the center number of 19x19 Magic Square is 181, also a prime number. This is why the 19x19 Magic Square Luo Shu would be a good place to look for an order of prime numbers within the trillions of magic square possiblities.

Magic Squares constructed in the Luo Shu format
offer the most balanced and harmonic way to arrange numbers. These arrangements were meant to assist humankind to evolve and prosper.

Another interesting feature of the 19x19 Magic Square is the triabolo that links this magic square with the 9x9 Magic Square.

See the below link:

for more on the 19x19 Magic Square

Monday, April 19, 2010


Magic Square Contest #2

This is a contest for the construction of magic squares with squares or cubes of pure integers as the major components of the square. The standard definition applies: all columns, rows, and diagonals must add up to the same number, known as the constant of the square.

The smallest possible constant for a 4x4 magic square of squares is this square first constructed by Andrew Bremner, with the constant = 2823.

There are six different competitions that involve different size squares and other variables.

Does a 3x3 Magic Square composed only of squared integers exist?

THIS IS CRAZY - WHO WOULD EVER HAVE THUNK THIS!!!!! I love magic square nerds, rock on!!!!


Did you know that Lady GaGa is into magic squares?


Thursday, April 15, 2010

Leonardo Da Vinci and the Magic Square

Leonardo da Vinci explored the incorporation of Math, architecture, and ground plans for church design in the late 15th century. Da Vinci used the Lo Shu as a model for the quincunx church design.

Donato Brammante also incorporated the Magic Square in his ground plans for St. Peter’s Basilica. Brammante and da Vinci knew each other well and collaborated on projects. Both Brammante and da Vinci were greatly influenced by Luca Pacioli, who was known to possess a set of magic squares and reputedly knew about sacred geometry.

Albrecth Durer specifically sought out Pacioli for this knowledge. Da Vinci lived with Pacioli and provided the illustrations to Pacioli’s book, The Divine Proportion.

The concept of incorporating the square, circle, and right triangle with the four cardinal directions and sacred Math has always been intriguing to artists, architects, and Mathematicians for millennia.

These concepts were employed in Southeast Asia and China for thousands of years prior to the Italian Renaissance to mark the cosmic center of the universe, the axis mundi.

The mathematical symbolism of the Stupa and Chinese temple design may have had a great influence on early Byzantine church design that borrowed the quincunx pattern.

Tuesday, April 13, 2010

The Magic Square and Chinese Talismans

This Chinese Talisman (approx. 2,000 years old) demonstrates the use of the Luo Shu Magic Square as a template for Chinese ritual talismans. The square and the circle represent earth and Heaven, female and male, yin and yang.

The Luo Shu model was commonly incorporated in the fabrication of TLV Bronze mirrors and the Chinese bi disc, as well as the Ming Tang temple.

This is also the ground plan for early Byzantine church design known as the quincunx or cross in square design. Leonardo da Vinci (church drawings), Brammante (St. Peter's Basilica), and Placidio (Villa Capri) used this design and were probably influenced by Luca Pacioli.

There exists a school of thought that supports an influence of Chinese iconograpahy and cosmology (divining and the Yi Jing) with early Christian art and architecture.

Monday, April 12, 2010

Magic Square Contest


James Youlton from Victorville, California has mostly been leading this contest thus far. However, he is now getting a serious challenge from Marcin Mucha (Poland) and Hermann Jurksch (Germany). The Germans are favored to do well here. Garr Godrey (Seattle) is fourth and all four contestants are within 0.04 points of one another. WOW!!!

One reader of the blog has informed me that some of my reporting is incorrect concerning the languages/algorithms/environments that are receiving mention.

Brainf*** has been talked about - it is a programming language known for its extreme minimalism and would be difficult to use in this contest. Brainf*** should be removed from the preferred list.

PowerShell is a scripting language for Windows and probably should not have been on the preferred list.

What seems to be clear is that the key to this contest is the algorithm selected and the diligence of the operator. Most languages should be able to implement a good algorithm.

Sunday, April 11, 2010


Water Retention Magic Square contest at:

What is a magic square:

What is a water retention magic square:

The contest has attracted 130 participants from 29 countries. The discussion board gives an interesting look into the minds of some brilliant computer programmers. One enjoyable debate is which programming language is the best suited for the contest.

What I have been able to glean so far, though not a programmer; is that there is no perfect language or development environment. An individual's genius and focus is what yield results. Some computer languages appear more suitable for this competition. From the discussion board commentary:

Prefered languages/environments/algorithm:
Turbo Pascal (outdated?)
C #
Brainfuck: no kidding, that is the name: reputed to be one of the simplest languages.
zetagrid algorithm

Languages/environments lacking: