A mystical magic square is a special kind of magic square that not only follows the rules of a regular magic square but also has additional properties that make it unique and fascinating. In a traditional magic square, the numbers in each row, column, and diagonal add up to the same sum. However, in a mystical magic square, these conditions are enhanced further, resulting in a square that has even more intriguing properties. One notable characteristic of a mystical magic square is that it contains a hidden pattern or symbol when the numbers are arranged in a specific way. This pattern or symbol often holds a significant meaning or represents a particular concept, making it a source of fascination for those who study or encounter mystical magic squares. Furthermore, mystical magic squares often exhibit other mystical properties, such as having a specific numerical pattern or arrangement that adds to their allure.
In This Article
Seashells, animal horns, and the cochlea of the ear are logarithmic spirals that can be generated using a mathematical constant known as the golden ratio. Agrippa believed that a magic square containing the digit 1 which exhibits the magic constant of 1 in all directions represented God s eternal perfection.
Furthermore, mystical magic squares often exhibit other mystical properties, such as having a specific numerical pattern or arrangement that adds to their allure. These patterns can be based on mathematical formulas, geometric shapes, or symbolic representations, adding an element of mystery and intrigue to the square. Mystical magic squares have been studied and appreciated by various cultures and societies throughout history.
Pat'sBlog
I just came across an older article from the Journal of Recreational Mathematics about the 3x3 Magic square that reminded me of some beautiful relations in the square, and showed me a few I had never seen. The article is by Owen O'Shea and is titled "SOME WORDS ON THE LO SHU". If you want to search out the whole thing (well worth the read) it is in Volume 35(1) starting on page 23.
The Lo Shu Square ( literally: Luo (River) Book/Scroll) is the unique normal magic square of order three. Except for rotations or reflections it is the only order three magic square that can be formed with the digits 1-9. Chinese legends concerning the pre-historic Emperor Yu tell of the Lo Shu: In ancient China there was a huge deluge: the people offered sacrifices to the god of one of the flooding rivers, the Luo river, to try to calm his anger. A magical turtle emerged from the water with the curious and decidedly unnatural (for a turtle shell) Lo Shu pattern on its shell: circular dots giving unary (base 1) representations of the integers one through nine are arranged in a three-by-three grid. The representation in the more common Arabic Numerals looks like this:
The odd and even numbers alternate in the periphery of the Lo Shu pattern; the 4 even numbers are at the four corners, and the 5 odd numbers (outnumbering the even numbers by one) form a cross in the center of the square. The sums in each of the 3 rows, in each of the 3 columns, and in both diagonals, are all 15 (the number of days in each of the 24 cycles of the Chinese solar year.
Beyond the basics of the magic square, O'Shea points out several other interesting relations. First, the sum squares of the numbers in the top and bottom row are equal. 4 2 + 9 2 + 2 2 = 8 2 + 1 2 + 6 2 = 101. You can do the same thing with the two outside columns, 4 2 + 3 2 + 8 2 = 2 2 + 7 2 + 6 2 = 89. Go ahead, try the two diagonals, you now you are dying to know.
So what about the middle row and column? Well, the middle column is special; Because north is placed at the bottom of maps in China, the 3x3 magic square having number 1 at the bottom and 9 at the top is used in preference to the other rotations/reflections. As seen in the "Later Heaven" arrangement, 1 and 9 correspond with ☵ Kǎn 水 "Water" and ☲ Lí 火 "Fire" respectively. In the "Early Heaven" arrangement, they would correspond with ☷ Kūn 地 "Earth" and ☰ Qián 天 "Heaven" respectively. The 951 does have a nice numerical representation in the number. If you read the rows or columns as three digit numbers, you might notice that 492 – 357 + 816 = 951 and that 294 – 753 + 618 = 159. Kind of a transition from Heaven to Earth and back again.
An original O'Shea contribution is his discovery that, "Ignoring the middle column, form two-digit numbers with the other columns as follows: 42 + 37 + 86. These numbers sum to 165. Their sum of their
reversals, 68 + 73 + 24, is also 165. The same is true of 84 + 19 + 62 and their reversals, 26 + 91 + 48. Curiously, the sum of the squares of the odd digits, 1, 3, 5, 7, and 9, also equals 165."
If we go back to considering the rows as a three digit number, the square of each row numeral is the same as the square of their reversal: 492 2 + 357 2 + 816 2 = 618 2 + 753 2 + 294 2 . Of course that would be really impressive if it worked with the columns too. I mean, awesome impressive. ahh go on, try it.
The article goes on with several dozen interesting numerical relations, and if that's your thing, you should seek it out. I'll leave you with one last beauty:
There is a not too well know problem in math called the Tarry-Escott problem which asks if there are sets of integers with the same order (same number in each set) so that the integers in each set have the same sum, the same sum of squares, etc.up to and including the same sum of kth powers.
Remarkably, the pattern in the lo shu gives a solution to the Tarry-Escott problem. Starting at the top left and reading around the outside you get the four three digit numbers, 492 ,276 , 618 , 834 . Now read them going the other way round, 438, 816, 672, 294. Now add up the numbers in each set. Add up their squares. their cubes?
Historically, The magic squares appeared first in China. In 500
I do not think that anyone goes beyond the Indian people in terms of expecting help from magic squares for healing diseases and even finding a spouse. They also took first place in producing magic squares known as the Jaina inscriptions. The first 4x4 square was discovered on a door in Khajuraho, India, around 1100 AD (Figure 4). Jainism is an Indian philosophy that was established in the 6th century BC, which may imply how important magic squares are for Indians who follow this tradition.
They have been found in ancient civilizations like Egypt, China, and India, as well as in more recent times. The fascination with these squares stems from their intriguing mathematical properties, as well as the belief that they possess supernatural or mystical powers. Overall, a mystical magic square is a unique and enchanting variation of a regular magic square. Its hidden patterns, numerical arrangements, and symbolic representations make it a captivating subject for study and exploration. Whether seen as a mere mathematical curiosity or as a window into the mystical world, these squares continue to captivate and intrigue those who encounter them..
Reviews for "The Mystical Magic Square: Enhancing Intuition and Psychic Abilities"
1. John - 2 stars - Mystical magic square was not what I was expecting at all. The description made it seem like a fun and exciting puzzle game, but it turned out to be incredibly confusing. The instructions were unclear and the gameplay was frustrating. I spent more time trying to figure out how to play the game than actually enjoying it. I was definitely disappointed with my purchase.
2. Sarah - 1 star - Mystical magic square is a complete waste of time. The graphics are outdated and the gameplay is extremely repetitive. I found myself quickly losing interest in the game and becoming bored. Additionally, there were several glitches and bugs that made it difficult to progress. I wouldn't recommend this game to anyone.
3. Michael - 2 stars - I had high hopes for Mystical magic square, but it fell short in many areas. The puzzles were too easy and became repetitive after a while. The lack of variety and challenge made the game boring after just a couple of hours of play. The storyline was also quite predictable and cliché. Overall, it didn't live up to the hype and I wouldn't play it again.
4. Emily - 3 stars - While Mystical magic square had its moments, I found it to be underwhelming. The gameplay mechanics were clunky and the controls were difficult to master. The levels became increasingly frustrating and I didn't feel a sense of accomplishment when I finally completed them. The concept had potential, but the execution was lacking in my opinion.