The Magic Square Blog: 2026

The Chinese Magic Square has always been known to have correspondences with Time and Space. This post will demonstrate how the 13x13 magic square and the 27x27 magic square communicate the numbers associated with the keeping of time and therefore were integral to the foundation of Chinese metaphysics. We start with the 13x13 magic square, the numbers of the calendar, and conclude with the grand daddy of all magic squares, the 27x27 magic square in the Luo Shu format.

THE 13X13 MAGIC SQUARE

Table 1. The significant numbers of the 13x13 magic square are highlighted in red, Pythagorean triplets highlighted in purple. The magic constant of the square is 13 x 85 = 1,105. Significant numbers of any magic square in the Luo Shu format will occupy these positions. One can see the Pythagorean triplet of numbers for the 15x15 magic square. Note also the cross of odd numbers that occupy the vertical and horizontal axis.

If numbers are in fact a language, then the most important feature for numbers is to provide functional information about Time and Space. Magic squares in the Luo Shu format do exactly this.

THE NUMBER 13

The most important thing about the number 13 is that it is the seventh odd number.

The second most important thing about the number 13 is that it is part of the 13 – 84 – 85 Pythagorean triplet.

The most intriguing number is the number 7. The most important thing about the number 7 is its connection to the calendar (seven days in a week and cycles of seven).

The numbers 13 and 85 are the result of the difference and addition of the squares of two consecutive numbers.

(7x7) - (6x6) = 49 – 36 = 13 (the order of the square) and adding the squares generates:

(7x7) + (6x6) = 49 + 36 = 85 (the center number of the square).

These numbers, 13 and 85, represent the odd numbers of the 13 – 84 – 85 Pythagorean triplet.

The sum of all the numbers one through 13 equals 91. This is a most important number that corresponds to the calendar as there are 91 days in a season.

The following odd numbers are numbers that describe Time and Space. Time as in the numbers of the calendar and Space as in the Pythagorean Theorem:

7 – the number of days in a week
13 – the number of weeks in a season and part of the 13, 84, 85 Pythagorean triplet
85 – part of the 13, 84, 85 Pythagorean triplet
91 – the number of days in a season
169 - part of the 13, 84, 85 Pythagorean theorem

These same numbers are the significant numbers of the 13x13 magic square.

7 – is the odd component of the square, which is based on 6 & 7
13 – is the size or order of the square
85 – is the center number of 1 thru 169 and is the center number of the square
91 – is the sum of the numbers 1 thru 13
169 - the 13x13 magic square in the Luo Shu format is the arrangement of the first 169 numbers in this square
And most important, these numbers add up to 365 - the number of days in the solar cycle, linking the significant numbers of the 13x13 magic square with the center number of the 27x27 magic square.

These five significant numbers of the 13x13 magic square (7, 13, 85, 91, and 169) also form a triabolo in the 27x27 magic square.

THE TRIABOLO

Table 2. The 27x27 magic square (the square of the sun) demonstrating the triabolo of numbers that represent the significant numbers of the 13x13 magic square thus linking the two squares that make calendrical correspondences. The magic constant of this square is 27 x 365 = 9,855. Note also the cross of odd numbers that occupy the vertical and horizontal axis.

The 27x27 magic square is based on the numbrers 13 and 14:

(14x14) - (13x13) = 196 - 169 = 27 (the order of the square) and (14x14) + (13x13) = 196 + 169 = 365 ( the center number of the square).

The numbers 13, 27, 378 (the sum of the numbers 1 thru 27), 365 and 729 (27x27) represent the signifcant numbers of the 27x27 magic square. All magic squares in the Luo Shu format have their significant numbers in the same relative position, only select magic squares will have a self contained triabolo of numbers representing this concept: the 11x11magic square, the 19x19 magic square, and the 27x27 magic square have triabolos with the 11x11 magic square having a triabolo of numbers that correspond to the 5x5 magic square; and the 19x19 magic square having a triabolo of numbers that correspond to the 9x9 magic square; and the 27x27 magic square having a triabolo of numbers that correspond to the 13x13 magic square. Only odd numbers are involved.

The triabolo is a geometric shape the links the significant numbers of one magic square with a larger magic square. The 27x27 magic square is the most superior of all magic squares as it has the numbers of the calendar, as does the 13x13 magic square, but also has the number 365 as its center number. Plato refers to this important square in his book The Republic , chapter nine when Socrates states, "a king who rules with wisdom lives exactly 729 times more pleasantly than one who rules through tyranny" (find section 293, footnote 3, scroll down about three quarters of the script). The number 729 is 27 squared, or the square of 27, that is to say, the 27x27 magic square with 365 as it's center number. Read the entire paragraph and you will see that Socrates refers to the calendar as well. Man is the beast, he is wisdom, and wisdom is the understanding of nature and the numbers that rule the universe. His number is 666, the sum total of all the numbers in the 6x6 magic square, one thru thirty six, the square of the sun.

Conclusion

1. The 13x13 and 27x27 magic squares in the Luo Shu format are related to Time as in the numbers of the calendar, and Space as in the Pythagorean Theorem.

2. The number seven plays a key role.

3. Odd numbers have a higher status than even numbers.

4. Odd numbers are created by taking the difference of the squares of two consecutive numbers, eg:

(1x1) - (0x0) = 1
(2x2) - (1x1) = 3

(3x3) - (2x2) = 5

(4x4) - (3x3) = 7

5. The center number of Luo Shu format magic squares are created by taking the sum of the squares of two consecutive numbers:

(1x1) + (0x0) = 1, no magic squre
(2x2) + (1x1) = 5; center of the order 3 magic square

(3x3) + (2x2) = 13, center of the order 5 magic square

(4x4) + (3x3) = 25. center of the order 7 magic square

6. The Chinese magic square is the perfect model of Time and Space and is symbolic of establishing order thru the application of functional mathematics. The symbols that result have survived in civilization for over three thousand years. This blog is dedicated to the understanding of the math and symbols generated from the Luo Shu, a complicated but understandable "set of magic squares".

The mosaics of Ravenna, Italy were a major influence to Gustav Klimt. This paper will demonstrate the specific mosaics that provided the usage of symbols demonstrated in The Lady in Gold.

It is well documentated that in 1903 Klimt visited Ravenna with fellow artist Maximilian Lenz. Lenz reported that “the mosaics made an immense decisive impression on Klimt. From this comes the resplendence, the stiff decoration of his art” (Robert Nelson, Modernism’s Byzantium Byzantium’s Modernism, 2015).

Klimt himself stated that “the mosaics of unbelievable splendour were a revelation” (Anne-Marie O’Connor, The Lady in Gold: The Extraordinary Tale of Gustav Klimt’s Masterpiece, Bloch-Bauer, 2015).

It is widely accepted that the mosaic of Empress Theodora from the Basilica of San Vitale in Ravenna was the model from which the painting of The Lady in Gold was based upon.

Image 1. Left: Detail of Empress Theodora, c. 540, San Vitale, Ravenna. Right: Klimt’s Lady in Gold, c. 1907, Neue Galerie, New York. Note the use of red paint in The Lady of God..

What is not well known, or not known at all, is the symbolism used that is highlighted in red in Klimt’s painting. This is the only use of red in Klimt’s Lady in Gold.

Image 2. Mosaic from Sant’ Apollonare Nuovo, c. 525 demonstrating quincuncial symbolism.

Image 3. Left: Detail of mosaic from Sant’ Apollonare Nuovo, c. 525. Right: detail of quincunx symbol used in Lady in Gold.

Quincuncial composition represented extremely important symbolism and was used repetitively in early Christian art and architecture. This subject has been treated with great detail in earlier posts within this blog and in the author’s paper, The Secret of the Magic Square: Numerology in Art and Architecture and Paloma Pajares-Ayuela's book, Cosmatesque Ornament, 2001).

The early church used quincuncial composition to identify things of religious importance such as sacred books as well as church design (example: the quincunx groundplan).

Image 4. Examples of the use of the quincunx pattern dating from the 6th to the 11th centuries, demonstrating the consistent use of quincuncial composition and variations thereof. Reading from the upper left to right: (a) Mosaic of garment from San Vitale, c. 550 AD; (b) Book cover of Lindau Gospels, lower cover, c. 800 AD; (c) Book cover of Lindau Gospels, upper cover, c. 875 AD; (d) Book cover of Christ and the Virgin Orans (Treasury of San Marcos), c. tenth century; (e) Detail from the ivory throne of Archbishop Maximianus demonstrating book cover, Ravenna, Italy, c. 550 AD; (f) Mosaic of book cover from Sant’ Apollinare Nuovo, c. sixth century; (g) Coptic Gospels book cover from Fayum, Egypt, c. seventh century; (h) Detail of metal work from a glass amphora from the Treasury of San Marcos, c. eleventh century; (i) Detail of turquoise glass bowl and metal work from the Treasury of San Marcos, c. tenth century. Quincuncial geometry also appeared in the ground plans for church design. (Artist: Sam Steigmeier, from the book by Robert Dickter, Number Time Archetype, 2014).

Quincunx symbolism represents the establishment of universal order thru the functional use of mathematics. There is no evidence to support that Gustav Klimt was aware of the mathematical influence of quincuncial composition used in early Christian art and architecture. It is more likely that Klimt was aware of the consistent usage of this symbol throughout the history of art and architecture especially from the mosaics in Ravenna, Italy.