Magic of Squares: Power Point Presentation
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Physics Department,
Panskura Banamali College
Magic of SquaresMagic of SquaresAbhijit Kar GuptaAbhijit Kar Gupta
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Square:
a
2aaa Area =
Square Network:
To begin with…To begin with…
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First lesson in Algebra:First lesson in Algebra:
a
b
abbaba 2)( 222
A Jigsaw puzzleA Jigsaw puzzle
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Square of a NumberSquare of a Number::
2112231
23531 247531
2597531
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The Journey of a theorem…The Journey of a theorem…
Babylon (1900 – 1600 BC)Babylon (1900 – 1600 BC)
Pythagoras (560 – 480 BC)Pythagoras (560 – 480 BC)
Pierre de Fermat (1630)Pierre de Fermat (1630)
Andrew Wiles (1993)Andrew Wiles (1993)
222 zyx
,nnn zyx 2n
Proved Fermat’s Last Proved Fermat’s Last TheoremTheorem
probably discovered the proofprobably discovered the proof
(Fermat’s Last Theorem(Fermat’s Last Theorem))
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Indefinitely Perforated SquareIndefinitely Perforated SquareFractal Geometry
Go on repeating the process…Go on repeating the process…
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The game of The game of ChessChess
and and crossword puzzle…crossword puzzle…
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The Fifteen The Fifteen PuzzlePuzzle
Sam Lyod,Sam Lyod,
late 1870slate 1870s
In America…In America… 11 22 33 44
55 66 77 88
99 1010 1111 1212
1313 1515 1414
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Magic Magic SquareSquare
3x3 Magic Square3x3 Magic Square
Magic Sum = 15Magic Sum = 15
Made in China‘‘Lo Shu’Lo Shu’
2000 BC2000 BC
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A Magic Square:A Magic Square:
Magic Sum = 34Magic Sum = 34
Temples ofTemples of KhajurahoKhajuraho1212thth Century AD Century AD
77 1212 11 1414
2 2 1313 88 1111
1616 3 3
1010 55
99 66 1515 44
44
Made in India
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77 1212 11 1414 77 1212 11 1414
2 2 1313 88 1111 2 2 1313 88 1111 1616 3 3
1010 55 1616 3 3
1010 55
99 66 1515 44 99 66 1515 44
77 1212 11 1414 77 1212 11 1414 2 2 1313 88 1111 2 2 1313 88 1111 1616 3 3
1010 55 1616 3 3
1010 55
99 66 1515 44 99 66 1515 44
Magic Carpet
Add up any 4 numbers in a line:Add up any 4 numbers in a line:
horizontal, vertical or diagonal, you get the magic sum = 34.horizontal, vertical or diagonal, you get the magic sum = 34.
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Franklin Squares:Franklin Squares:
‘…‘…the most magically magic square ever made by a magician’the most magically magic square ever made by a magician’
- - Benjamin FranklinBenjamin Franklin
88
1616 and magic squares and and magic squares and magicmagic carpets,carpets,
more interesting properties…more interesting properties…
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And the Fun ride…And the Fun ride…
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Back to square one…Back to square one…