The connections between Chess and Mathematics chess...
Transcript of The connections between Chess and Mathematics chess...
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David Wells
The connections between chess and mathematics
Chess and Mathematics Conference, London,6th December 2014
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Connections❖ Philosophical
❖ Mathematical Recreations
❖ Tactics and Strategy
❖ Proof and Proving
❖ Creativity
❖ Complete Analysis
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Philosophical
It is much like a piece in chess - its nature is defined by simple rules
What is the number 2?
If the whole class learn chess, they will all move the pieces in the same way: total agreement.
When they master elementary arithmetic they will all operate with integers in the same way.
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Mathematical RecreationsPentominoes
Mathematical and playful
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PentominoesGolomb’s Game
Pentominoes are mathematical objects yet Golomb's game is a perfect example of an abstract game: spot the cross-over.
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Tactics and Strategieswith Fox and Hounds
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Proof and ProvingNoughts and Crosses
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Create your own GameJohn Conway's Phutball
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Create ProblemsChess
White to play and draw
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Complete AnalysisCorner Game
The rook can only move up or right - any number of squares
Move here to win
Take turns to move rook
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Corner GameShirley Clarke (1988)
'This kind of maths is so exciting for children. As Jermaine was writing his 'ideas for new rules', Nicholas was compulsively trying out his own ideas'.
"[this] theory about games seems to be true! The children started off by experimenting to test their theories but, in playing the game, it gradually dawned on them that there were mathematical reasons behind what was happening; they had moved on to the idea of proof."
Jermaine and Nicholas
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Children’s observations"We were testing to see if the person who played first won.
As we were testing we found that if the player moved the rook onto the diagonal line you will always win.
Now we know this, the test is over because if you move first the other player will win because they go straight to the diagonal line."
Not interested in playing once the game was solved
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Children’s Ideas for New Rules
Move only one square at a time or two squares
at a time.
Start only on white
Change the piece to bishop, king, queen, knight
You don’t have to move nearer to the
target square
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Tower of Hanoi
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– David Hilbert
“Mathematics is a game played according to certain simple rules with meaningless marks on paper.”
“Games may have the potential to provide students with a mathematically focused activity while engaging them through a perception of fun.”
– Leicha Bragg
FALSE
TRUE