Magic Squares

Magic SquaresDebunking the MagicRadu Sorici

The University of Texas at Dallas{Random Magic Square

No practical use yet great influence upon people

No practical use yet great influence upon people

In Mathematics we study the nature of numbers and magic squares are a perfect example to show their natural symmetryHistory is Very ImportantThere is evidence to date magic squares as early as the 6th century due to Chinese mathematiciansHistory is Very ImportantThere is evidence to date magic squares as early as the 6th century due to Chinese mathematiciansIt was later discovered by the Arabs in the 7th centuryHistory is Very ImportantThere is evidence to date magic squares as early as the 6th century due to Chinese mathematiciansIt was later discovered by the Arabs in the 7th centuryThe Lo Shu square is the first recorded magic square

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History is Very ImportantThere is evidence to date magic squares as early as the 6th century due to Chinese mathematiciansIt was later discovered by the Arabs in the 7th centuryThe Lo Shu square is the first recorded magic square

The sum in each row, column, diagonal is 15 which is the number of days in each of the 24 cycles of the Chinese solar year

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History is Very ImportantThere is evidence to date magic squares as early as the 6th century due to Chinese mathematiciansIt was later discovered by the Arabs in the 7th centuryThe Lo Shu square is the first recorded magic square

The sum in each row, column, diagonal is 15 which is the number of days in each of the 24 cycles of the Chinese solar yearMagic squares have cultural aspects to them as well, for example they were worn as talismans by people in Egypt and India. It went as far as being attributed mythical properties. (Thank you Wikipedia for great information)

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So what exactly is a Magic Square?So what exactly is a Magic Square?So what exactly is a Magic Square?So what exactly is a Magic Square?So what exactly is a Magic Square?So what exactly is a Magic Square?So what exactly is a Magic Square?

So what exactly is a Magic Square?

Before we StartBefore we StartBefore we StartBefore we Start

Types of Magic SquaresConstruction MethodsOdd orders (De la Loubre)Construction Methods

Odd orders (De la Loubre)Construction MethodsOdd orders

Construction MethodsConstruction Methods

Construction MethodsSingly EvenThe Ralph Strachey MethodConstruction Methods

ACDBConstruction Methods

Construction MethodsSingly EvenThe Ralph Strachey Method3rd Step - Exchange the middle cell of the leftmost column of subsquare A with the corresponding cell of subsquare D. Exchange the central cell in subsquare A with the corresponding cell of subsquare D

What Now?Panmagic SquareA panmagic(also called diabolical) square is a magic square with the additional property that the broken diagonals also add up to the magic constant.Panmagic Square

Panmagic Square

Panmagic Square

Panmagic Square Continued5 by 5 panmagic squares introduces even more magicPanmagic Square Continued5 by 5 panmagic squares introduces even more magic quincunx

17+25+13+1+9=6521+7+13+19+5=654+10+13+16+22=6520+2+13+24+6=65

Magic CubeA magic cube is a magic square but in 3-D. All of the properties are translated to 3-D.Magic CubeMagic CubeMagic Cube

Bimagic SquareA Bimagic Square is a magic square that is also a magic square if all of its numbers are squaredBimagic SquareA Bimagic Square is a magic square that is also a magic square if all of its numbers are squaredThe first known bimagic square is of order 8Bimagic SquareA Bimagic Square is a magic square that is also a magic square if all of its numbers are squaredThe first known bimagic square is of order 8It has been shown that all 3 by 3 bimagic squares are trivialBimagic Square

Multiplication Magic SquareA square which is magic under multiplication is called a multiplication magic square. The magic constants increase very fast with the order of the square.Multiplication Magic SquareA square which is magic under multiplication is called a multiplication magic square. The magic constants increase very fast with the order of the square.For orders 3 and 4 the following are the smallest multiplication magic squares

Word SquareA set of words having the same number of letters; when the words are written in a square grid horizontally, the same set of words can be read vertically Word SquareA set of words having the same number of letters; when the words are written in a square grid horizontally, the same set of words can be read vertically Because we speak English we are naturally interested in the ones made of English wordsWord SquareA set of words having the same number of letters; when the words are written in a square grid horizontally, the same set of words can be read vertically Because we speak English we are naturally interested in the ones made of English wordsThere are word squares of order 3 through 9 (cases 3, 4, 9 are displayed below)

B I T C A R D A C H A L A S I AI C E A R E A C R E N I D E N ST E N R E A R H E X A N D R I CD A R T A N A B O L I T E L I N O L E N I N A D D L E H E A D S E R I N E T T E I N I T I A T O R A S C E N D E R S

The hunt for a word square of order 10 is still going and apparently it has been called the holy grail of logology.Fibonacci Magic SquareThe presentation would not be complete with a reference to the Fibonacci numbersFibonacci Magic SquareThe presentation would not be complete with a reference to the Fibonacci numbersStart with the basic 3 by 3 magic square

Fibonacci Magic SquareThe presentation would not be complete with a reference to the Fibonacci numbersStart with the basic 3 by 3 magic square

Replace each number with its corresponding Fibonacci number

Fibonacci Magic SquareThe presentation would not be complete with a reference to the Fibonacci numbersStart with the basic 3 by 3 magic square

Replace each number with its corresponding Fibonacci number

Even though this is not a magic square it so happens that the sum of the products of the three rows is equal to the sum of the products of the three columns.

Random Magic Square

Final WordsMasonic Cipher

Final WordsMasonic Cipher

Durer Magic SquareFinal WordsThe message is

Final WordsThe message is

I Love Mathematics