A magic square of square is a type of magic square where the numbers in the square form a perfect square when added together horizontally, vertically, and diagonally. This means that the sum of the numbers in each row, column, and diagonal will be the same. It is also known as a pandiagonal magic square. In a magic square of square, the numbers are arranged in a square grid in such a way that the sum of the numbers in each row, column, and diagonal is equal to the same value, which is equal to the sum of the square root of the number of cells in the square. For example, in a 4x4 magic square of square, the sum of the numbers in each row, column, and diagonal would be equal to 4 + 4 = 8. The concept of magic squares of square has been known since ancient times and has been a topic of interest for many mathematicians and scholars.
Students can also research how to make magic squares (there are algorithms) or learn more about Franklin’s work on magic squares; one of the best books on that topic is Benjamin Franklin’s Numbers: An Unsung Mathematical Odyssey by Paul C. Pasles. The American Mathematical Monthly has published numerous articles on Franklin's magic squares, including Pasles's 2001 "The Lost Squares of Dr. Franklin: Ben Franklin's Missing Squares and the Secret of the Magic Circle" and Christopher J. Henrich's "Magic Squares and Linear Algebra." Another article on magic squares in Convergence is P. G. Brown's "The Magic Squares of Manuel Moschopoulos."
The four corner numbers in the great square added to the four central numbers, make 1028, equal to half the sum of any vertical or horizontal column, which contains 16 numbers, and equal to half a diagonal or its parallel. James Parton 1822 1891 discussed the origin of Benjamin Franklin s 16X16 Magic Square of Squares in his biography, Life and Times of Benjamin Franklin pp.
The concept of magic squares of square has been known since ancient times and has been a topic of interest for many mathematicians and scholars. There are various methods and algorithms that can be used to construct a magic square of square, including the Siamese method, the Strachey method, and the De La Loubère method, among others. Magic squares of square have applications in various fields, including mathematics, puzzles, and even art.
The Patchery Menagerie
I freely confess to sucking at basic Math, even though I get the gist of it. I need a calculator to add stuff up properly. I can't look at a string of numbers and add them up to get an exact total in my head, but I can look at them and get damned close. I find numbers interesting. Whole numbers, anyway. Once you get into sines and cosines, and pi and all that other stuff, I'm totally lost and I lose interest. What interests me about numbers is the rhythm they have. I can't explain it any better than that.
This is a MAGIC SQUARE. Go ahead, look it up.
Here's a summary: In recreational mathematics and combinatorial design, a magic square is a square grid filled with distinct positive integers in the range such that each cell contains a different integer and the sum of the integers in each row, column and diagonal is equal.
So first of all, look at the numbers in the photo above. You can see the numbers 1 to 16 shown once each. Now add the numbers across in each row. Total = 34. Now add up the numbers in each column. Total = 34. Now add up the diagonals. Total = 34. Each group of four adjacent numbers also adds up to 34. Pretty cool huh?
This particular Magic Square is a Pan-diagonal Magic Square, meaning the broken diagonals still add up to 34 (2+12+15+5, for example). It was inscribed on the wall of Parshvanath temple in Khajuraho India in the 12th Century. It is known as the Chautisa Yantra since its magic sum is 34. It is also a "Most-Perfect Magic Square," but I confess I don't understand enough math to know why.
Still though I think it's pretty neat and I have the page with the numbers above tacked onto inspiration wall in my studio. I am thinking of making a small quilt that is a magic square. I'll use my free-pieced technique to make the numbers, of course, and I'll have to work out how big the squares around them will be, but it's pretty clear to me the numbers have to look consistent with each other and that the fabrics that comprise the numbers and the backgrounds can't be TOO busy.
I don't know if I will install a grid between the numbers, as one of my favorite artists, Albrecht Durer, did in this one, in his famous engraving Melencolia I, from 1514.
I like the idea of not being particularly descriptive with any other information about what makes it a Magic Square. (Translation: this blog post will have everything I want to say about Magic Squares, but anybody who sees the quilt hanging somewhere won't get it unless they look at the numbers and start adding them up in their heads, or if they happen to know what a magic square is.)
- A 2x2 magic square cannot be constructed.
- There is only ONE 3x3 Magic Square
- There are exactly 880 4x4 Magic Squares.
- I must be what is considered a "recreational mathematician."
"A Magic Square of Squares," Gentleman's Magazine (July 1768), pp. 312–313.
They are often used as brain teasers, and their symmetry and aesthetic appeal make them popular designs for art and decoration. In mathematics, the study of magic squares and their properties is a well-established field. Overall, a magic square of square is a unique type of magic square where the numbers form a perfect square when added together horizontally, vertically, and diagonally. Its properties and construction methods have fascinated mathematicians and puzzle enthusiasts for centuries..
Reviews for "The role of magic squares in modern cryptography"
1. John - 2 stars - I was really excited to try "Magic square of square" but I was disappointed with the game. The graphics were outdated and the gameplay was repetitive. There was also a lack of variety in the levels and puzzles. Overall, I found the game to be quite boring and not worth the time or money.
2. Sarah - 1 star - "Magic square of square" is one of the worst games I have ever played. The controls were clunky and unresponsive, making it frustrating to play. The levels were also poorly designed, with confusing layouts and unclear objectives. The game also crashed multiple times, causing me to lose progress. I would not recommend this game to anyone.
3. David - 2 stars - I was expecting a challenging puzzle game with "Magic square of square", but instead, I found it to be incredibly easy and repetitive. The puzzles lacked creativity and became monotonous after a few levels. Additionally, the game had numerous bugs and glitches that hindered the overall experience. I was disappointed with this game and would not play it again.
4. Emma - 1 star - "Magic square of square" was a complete waste of time. The graphics were outdated and low-quality. The gameplay was dull and offered no excitement or challenge. There was no storyline or narrative to keep me engaged. Overall, it was a boring and forgettable game that I regret playing.
5. Michael - 2 stars - I had high expectations for "Magic square of square" but it fell short in many aspects. The game lacked originality and innovation, feeling like a generic puzzle game. The controls were also difficult to master, leading to frustration. It didn't offer anything new or exciting, and I quickly lost interest. I wouldn't recommend this game to puzzle game enthusiasts.