““The Proof” Video and The Proof” Video and ProjectProject

Objectives:

1.To watch and discuss NOVA’s “The Proof”

2.To research and present various unproven mathematical conjectures

Fermat’s Last TheoremFermat’s Last Theorem

For an integer n > 2, there exists no nonzero integer solutions to the equation

nnn cba What does this equation look like?

The Pythagorean TheoremThe Pythagorean Theorem

In a right triangle, if a and b are the lengths of the legs and c is the length of the hypotenuse, then a2 + b2 = c2.

Can you name any whole number solutions to this equation?

These are called Pythagorean Triples.

Example 1Example 1

How many examples would you have to check to prove Fermat’s Last Theorem?

How many examples would you have to find to disprove it?

Andrew WilesAndrew Wiles

While working at Princeton University, this handsome gentleman was the first to give a deductive proof for Fermat’s Last Theorem, which technically was a conjecture before Wiles’s proof.

For Love or Money?For Love or Money?

In “The Proof” Wiles said that when he completed his proof, there was a moment when he knew something that the rest of the human race did not. For some this would be reason enough to do anything.

For Love or Money?For Love or Money?

For others, that feeling would need to augmented by lots of green pieces of paper. So in addition to fulfilling his life dream, Wiles was also awarded the Shaw Prize in 2005, amounting to $1 million.

Nova’s “The Proof”Nova’s “The Proof”

Follow the links below to watch “The Proof” on YouTube.

WarningWarning: I cannot control the asinine things that people write in the comments section, so beware!

Nova’s “The Proof”Nova’s “The Proof”

Follow the links below to watch “The Proof” on YouTube.

• Part 1• Part 2• Part 3• Part 4• Part 5

Project: DescriptionProject: Description

Individually, you will be creating a PowerPoint Presentation or a poster that will explain the role of reasoning in mathematics and highlight a particular theorem and an unproven conjecture. It will be worth a test grade and will be due November 3.

Project: DescriptionProject: Description

Here is a list of items your project must contain:

1.Explanation of the relationship between inductive and deductive reasoning

2.Explanation of the relationship between conjectures, theorems, and proof

3.Description of a mathematical theorem with any appropriate illustrations, examples, applications

Project: DescriptionProject: Description

4. Description of a famous mathematical conjecture with any appropriate illustrations or examples– Who formulated it?

– Why can’t it be proven by testing examples?

– How can it be disproven?

5. Works Cited with hyperlinks

Turning In Your ProjectTurning In Your Project

• Poster– Bring it to class on 11/3– Works Cited on the back

• PowerPoint– Email a copy to jnoel@dentonisd.org by 11/3– Print a Handout to turn in on 11/3– You might bring a backup copy just in case

Printing a HandoutPrinting a Handout

To print a Handout:

1.Choose Print as usual.

2.Under the Print what pull down menu, choose Handouts.

Printing a HandoutPrinting a Handout

3. Under the Slides per page drop down menu, choose 9.

4. (Optional): Click Preview and add a heading with your name under Print Options.

Project: WarningProject: Warning

Plagiarism is Plagiarism is punishable punishable by death!by death!