algebraic generalisation
DESCRIPTION
Algebraic generalisation. Unlock stories by generalising number properties. Why is this man so famous?. ANDREW WILES. Fermat’s last theorem. No positive integers satisfy the equation: n > 2. On doing mathematics…. - PowerPoint PPT PresentationTRANSCRIPT
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ALGEBRAIC GENERALISATION
Unlock stories by generalising number properties
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ANDREW WILES
Why is this man so famous?
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FERMAT’S LAST THEOREM
No positive integers satisfy the equation:
n > 2
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ON DOING MATHEMATICS…
Perhaps I can best describe my experience of doing mathematics in terms of a journey through a dark unexplored mansion.
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FINDING THE FURNITURE…
You enter the first room of the mansion and it's completely dark. You stumble around bumping into the furniture, but gradually you learn where each piece of furniture is.
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THE LIGHT GOES ON
Finally, after six months or so, you find the light switch, you turn it on, and suddenly it's all illuminated. You can see exactly where you were. Then you move into the next room and spend another six months in the dark.
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So each of these breakthroughs, while sometimes they're momentary, sometimes over a period of a day or two, they are the culmination of -- and couldn't exist without -- the many months of stumbling around in the dark that proceed them.
AFTER 7 YEARS WILES PROVED FERMAT’S LAST
THEOREM
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ALGEBRAIC GENERALISATION
Aim:
• To explore algebraic generalisations of number strategies
Success Criteria:
• I can generalise from a number strategy
• I can explain why an algebraic identity is always true
• I can use identities to manipulate algebraic expressions
• I know key algebra vocabulary and recording conventions
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EGG TECHNIQUE
E – Explain the strategy or method used to solve
the problem.
G – Give other examples that use the same
strategy or method.
G – Generalise – use algebra to show the
underlying structure.
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PROOFS
Show that the sum of consecutive
numbers is always odd
Show that the sum of three consecutive
numbers is always divisible by three
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SOPHIE GERMAIN
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OTHER FACTS
Took 358 years before it was proved
It took 7 years for Andrew Wiles to prove it
The proof is 150 pages long
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WHO IS NEW ZEALAND’S MOST FAMOUS
MATHEMATICIAN?
Vaughan Jones
Only winner of Fields medal (the mathematics equivalent of the Nobel Prize)
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HOW DID HE WIN IT?
Vaughan Jones was attending a conference in Mexico…
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His car broke down…
WHAT DO MATHEMATICIANS DO?
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He started looking at a dot pattern on the cover of a maths textbook…
WHAT DO MATHEMATICIANS DO?
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WHAT DO MATHEMATICIANS DO?
He began experimenting with the mathematics that he saw in the dot pattern…
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WHAT DO MATHEMATICIANS DO?
And noticed a link between the dots and knots…
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WHAT DO MATHEMATICIANS DO?
This lead to him developing a formula for describing knots:
V(T) = (1/t) (t – 1 – t – 3 – t – 1 + t – 2 + 1) = t – 4 + t – 3 + t – 1 Which is now called the Jones’ polynomial
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WHAT DO MATHEMATICIANS DO?
And he won the Fields Medal.
WOW!