““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 TheoremFor 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 TheoremIn 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 1How 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 WilesWhile 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: DescriptionIndividually, 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 September 28.

Project: DescriptionProject: DescriptionHere is a list of items your project must contain:1.Explanation of the relationship between

inductive and deductive reasoning2.Explanation of the relationship between

conjectures, theorems, and proof3.Description of a mathematical theorem with

any appropriate illustrations, examples, applications

Project: DescriptionProject: Description4. 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 by 9/28– Works Cited on the back

• PowerPoint– Email a copy to Ms. Bowden by 9/28– Print a Handout to turn in on 9/28– You might bring a backup copy just in case

Printing a HandoutPrinting a HandoutTo print a Handout:1.Choose Print as

usual.2.Under the Print

what pull down menu, choose Handouts.

Printing a HandoutPrinting a Handout3. 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!