Magic squares

Jai Ganesh · 2008-11-10 20:27:12

Just a thought....
Wouldn't it be nice to have a page on Magic Squares?

MathsIsFun · 2008-11-10 21:11:31

Good idea ... any one want to contribute ?

Jai Ganesh · 2008-11-17 02:08:07

Here's a 4x4 magic square of side total and diagonal total 34:-

Jai Ganesh · 2008-11-18 17:52:03

I found an interesting page on Magic Squares here. I believe we can put these magic squares of higher orders on the website.

MathsIsFun · 2008-11-18 18:09:05

I think it would be a great idea for you to Author a page on Magic Squares, ganesh!

Make it as fun as possible, so everyone can enjoy

Jai Ganesh · 2008-11-18 20:55:54

MathsIsFun,
I shall do it as you said.
But I am not adept at Graphics and that part of it has to be taken care by you.

MathsIsFun · 2008-11-18 20:58:33

Sure, I can do that part!

Jai Ganesh · 2008-11-24 22:06:43

Magic Squares

A magic square is a large square made up of n² smaller squares usually containing numbers 1 to n² such that the totals of all the rows, columns and the two diagonals are the same.

A magic square can re be rotated clockwise or anti-clockwise 90°, 180° or 270° and yet would retain its property. The second, third and fourth images are given to explain this point.

In ancient times such squares were thought to have magic properties, perhaps connected with the stars. Magic squares have been found in such widely divergent cultures as ancient China, Egypt, and India, as well as W Europe.

Magic squares have fascinated humanity throughout the ages, and have been around for over 4,000 years. They are found in a number of cultures, including Egypt and India, engraved on stone or metal and worn as talismans, the belief being that magic squares had astrological and divinatory qualities, their usage ensuring longevity and prevention of diseases.

Magic squares were known to Arab mathematicians, possibly as early as the 7th century, when the Arabs got into contact with Indian or South Asian culture, and learned Indian mathematics and astronomy, including other aspects of combinatorial mathematics. It has also been suggested that the idea came via China. The first magic squares of order 5 and 6 appear in an encyclopedia from Baghdad circa 983 AD, the Rasa'il Ihkwan al-Safa (the Encyclopedia of the Brethern of Purity); simpler magic squares were known to several earlier Arab mathematicians.

The Arab mathematician Al-Buni, who worked on magic squares around 1200 A.D., attributed mystical properties to them, although no details of these supposed properties are known. There are also references to the use of magic squares in astrological calculations, a practice that seems to have originated with the Arabs.

Certain extra restrictions can be imposed on magic squares. If not only the main diagonals but also the broken diagonals sum to the magic constant, the result is a panmagic square. If raising each number to certain powers yields another magic square, the result is a bimagic, a trimagic, or, in general, a multimagic square.

The side total or diagonal total of a magic square containing numbers from 1 to n² is given by the formula

.

However, magic squares can also be constructed using numbers 1+a to n²+a as given in the fifth magic square below which uses numbers from 2 to 10. In these cases, the side total or diagonal total of the magic square would be

The simplest magic square is that of the order 3 x 3. This is because a magic square containing the number 1 with no other squares cannot be said to be a magic square. The next option, a magic square of the order 2x2 does not exist because, for a magic square, the side total should be equal for different combinations of numbers. For any consecutive four numbers a,b,c, and d, only a+d=b+c and there are no other equalities whatever combination is tried.

Magic square 6 gives a magic square entirely comprising of prime numbers.
Rudolf Ondrejka (1928-2001) discovered the following 3x3 magic square of primes, in this case nine Chen primes:

Pictures 2 and 3 give you higher order magic squares such as 4x4, 5x5, and 6x6.

I shall soon add bigger magic squares to the list.

To
MathsIsFun:-
Please feel free to edit any portion of the first part of the page I am posting. If there is anything of particular interest you'd like to be added on the page, please let me know.

St.Dan-Marius · 2009-02-10 07:34:09

Anjali !

MathsIsFun · 2009-02-10 13:16:18

Ganesh: Sorry, I missed your post until now! I will get to work making it a web page soon

Jai Ganesh · 2009-02-12 03:43:19

Thanks, MathsIsFun!
I shall add bigger squares in this threa, which you may include in the page.
Regarding factorization of cubics, quartics etc., I shall post as early as I can. My work keeps me busy during weekends too

St.Dan-Marius · 2009-02-12 06:54:29

Hello!

MathsIsFun · 2009-02-12 08:37:32

Nice, St.Dan-Marius.

I like the shading too.

MathsIsFun · 2009-02-14 09:44:22

Ganesh: do you think you could re-write the start to be a little more fun-friendly? Something like "Magic squares are amazing ... look at this one ... if you add up the numbers they always total to ..."

Jai Ganesh · 2009-02-14 17:05:05

Sure, I shall, MathsIsFun! As a matter of fact, I wanted to rewrite the entire description...I shall do that in a million seconds from now, most certainly! I shall stick to the time limit this time

MathsIsFun · 2009-02-14 17:35:34

LOL

simron · 2009-02-17 11:33:16

I found a 12x12 magic square in a book I read the other day... maybe I'll find it and post it.

quittyqat · 2009-05-09 13:46:45

2 7 6
9 5 1
4 3 8

Math Is Fun Forum

#1 2008-11-10 20:27:12

Magic squares

#2 2008-11-10 21:11:31

Re: Magic squares

#3 2008-11-17 02:08:07

Re: Magic squares

#4 2008-11-18 17:52:03

Re: Magic squares

#5 2008-11-18 18:09:05

Re: Magic squares

#6 2008-11-18 20:55:54

Re: Magic squares

#7 2008-11-18 20:58:33

Re: Magic squares

#8 2008-11-24 22:06:43

Re: Magic squares

#9 2009-02-10 07:34:09

Re: Magic squares

#10 2009-02-10 13:16:18

Re: Magic squares

#11 2009-02-12 03:43:19

Re: Magic squares

#12 2009-02-12 06:54:29

Re: Magic squares

#13 2009-02-12 08:37:32

Re: Magic squares

#14 2009-02-14 09:44:22

Re: Magic squares

#15 2009-02-14 17:05:05

Re: Magic squares

#16 2009-02-14 17:35:34

Re: Magic squares

#17 2009-02-17 11:33:16

Re: Magic squares

#18 2009-05-09 13:46:45

Re: Magic squares

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