Magic Squares with professor Edward Brumgnach
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- čas přidán 4. 06. 2024
- A magic square is an arrangement of the integers in an MxM square matrix, with each integer occurring exactly once, and such that the sum of the entries of any row, any column, or any main diagonal is the same.
There are three types of magic squares: 1) M is an odd number (1, 3, 5, 7, etc.); these are referred to as “odd order” magic squares; 2) M is an even number divisible by both 2 and 4 (4, 8, 12, etc.); these are referred to as “doubly even order” magic squares; 3) M is an even number divisible by 2 but not by 4 (6, 10, 14, etc.); these are referred to as “singly even order” magic squares.
Over the past four thousand years numerous methods, some relatively simple and some fairly complex, for generating magic squares of the three different types have been described. I have devised a very simple method of forming any size “odd order” magic square. I named the method “Г + 2” (Gamma plus two) because this name describes the method. I also have generalized an existing procedure, proposed by Ralph Strachey in 1918, of generating “singly even order” magic squares. I called this the “Г + 2+Swap”, or less modestly the “Brumgnach-Strachey” method. I believe that my cell swap portion of the method is innovative and has not been described before. “Doubly even order” magic squares may be easily constructed by a method described by Albrecht Durer in 1514.
The paper describing these innovations is available at:
www.qcc.cuny.edu/engtech/ET_F...
He’s trying the best that he can to entertain and stimulate his bored and uninterested students. Great Professor
Watching this on the guys birthday!! Happy birthday student
Good evening Professor
Your method of teaching is amazing. For solving the Odd magic squares, I was taught by my college professor an even simpler method.
Always start at the top of the middle column and start filling the numbers in the cross diagonal towards NE . If you go out of the square on the top come down on the next column and follow the pattern. If you go out of square on the RHS, fold back on the left and continue.
If the immediate NE cell is busy, go down one cell and continue. It will be a smooth flow. Finally the last number will be on the bottom row middle cell. The start number will be in the middle column top cell and the last number will be in the middle column bottom cell
For example in a 5X5 square , number 1 will be in R1 C3. And number 25 will be in R5 C3.
I am very much pleased to view your video on magic squares and it is mind blowing. Please forgive me if I am wrong.
Thanking you sir
Baskaran R. From Tamil Nadu India
Kind sir,
Many thanks for such an entertaining monologue. I observe that "doubly even, singly even, and odd" (non-even?) hints at the insight that any side length can be thought of as a prime or composite integer, and that the factor of two(2) raised to some non-negative integer power (n) is always a component of that side length. From this perspective, n=0 is the class of ODD, n=1 corresponds to "singly-even", n=2 "doubly-even", in due course a power of n=12 might be described as "dodecahedraly-even" (with my apologies) and so on.
I myself have been playing at LoShu related squares in the last few days, and was delighted to produce an algorithm and code that was able to produce a 6561st order (8th-rank) LoShu Magic Square having a top-left cell value of 16,142,521 and characteristic linear and diagonal sum of 141,214,771,521.
I've not tried any higher-ranked LoShu squares as of yet, but it is indeed highly entertaining to see a 6561 by 6561 grid with these "Magic Square" properties comprised of every integer from 1 to 6561^2 inclusive. It is fun to imagine that any positive integer (just as it can be composed as a product of prime powers) can also be located within a 2-dimensional LoShu grid by two integers (row and column) easily, once those indices are converted to base-three notation.
At under ninety lines of code at the moment, it is functional, but I'm curious to see if the 2-D localization relation has a closed-form solution that will work for colossal squares in O(n^2). Beyond entertainment, I'm not sure what a 1,000,000th order LoShu Square would be good vor. 😉
Cheers!
THANK YOU I KNOW SO LITTLE IN THIS GOOD OPENER
Interesting stuff. But unfortunately all what you have said and talked about is in the Albuni's book, I don't know how to translate it exactly in English but something close, The main Source of Wisdom'. You'll find all what you're talking about and more. منبع اصول الحكمة in Arabic. You've mentioned Persia and India but you haven't mentioned Arabs I don't know the reason but I would encourage you to read more sir. In fact, there are so many Arab Scholars and Philosophers that wrote in this domain like Ghazali, Ibn Arabi, the famous Arab mathematician Jabir Ibn Hayyan and for your information it's from his name the word Algebra came from because he was the creator of Algebra, and many many more Muslim Mathematicians. These things had been into existence well before Mr Durer himself.
Great content THIS ONE CHANGED MY LIFE I AM A NUMEROLOGIST AND A MULTI- Millionaire thanks to numbers the language of ALL… who ever Reading this message o would like to send you peace and love… ASE TO THOSE ancestors that CAME BEFORE ME
Teach me sir
Ase! O Africa!
The professor failed to mentioned the more important part of that picture the figures in it had angelic wings depicting Angel's Professor?
Watching from Guyana. Interesting stuff. So, this is how Sudoku got it's start?
Nice
wonderful lecture bu what is the purpose of magic squares? is it useful? does it worth all your great efforts
?
No it’s not. That’s what mathematicians do for a living
The link to the website is not available
Hello,
Thank you for pointing this out, as the description and link were from the original 2008 posting on our internal media site.
Please try this link:
www.qcc.cuny.edu/engtech/ET_Faculty/Brumgnach/Magic_Squares/magicSquares1.html
Best,
Phillip Roncoroni
Digital Content Manager
how bout up and over is a triangle and triangles make up the square
5:37
ok
Old school ugly Google