Pythagorean Theorem

What is Your Favorite Proof of the Pythagorean Theorem?

A WebQuest for Geometry

You have all used the Theorem known as the Pythagorean Theorem. But where did this theorem come from? Who developed it? And, how do we know it will work for ALL right triangles? Are there other relationships related to the Pythagorean Theorem?

Maybe you've asked yourself these questions before. During this project you will have the opportunity to investigate and answer some of these questions, pose and investigate questions of your own and even attempt to develop your own original proof of the Pythagorean Theorem.

The Task

You and your partner need to investigate information about the Pythagorean Theorem and its proofs. (Yes, I said proofs. There are several proofs of the Pythagorean Theorem written by many different people.) Using the information you have gathered, you will present information on one proof of the Pythagorean Theorem, pose and investigate your own questions about other potential relationships (remember it is ok to find out that your conjecture may be false) and attempt to develop your own proof of the Pythagorean Theorem.

The Process

Part I:

You will be working with a partner during your investigation of the Pythagorean Theorem. You will be expected to do that work outside of class. You will be notified at the start of the project when your presentations/reports will be due.

Your project will contain the following:

1. An explanation of one of the proofs of the Pythagorean Theorem which will be presented to the class. You may use transparency paper, poster board, or a PowerPoint presentation to present your proof.

2. Pose two questions related to the Pythagorean Theorem and provide the solutions to these questions. Write a paragraph for each of the questions describing your experience and process while solving these questions. Potential questions could be:

What would happen if instead of squaring each side of the triangle, we cubed each side? Would a similar relationship hold true?
What happens if the triangle is not a right triangle?

(You may use one of the above as ONLY ONE of your two questions)

Part II:

Research will need to be conducted on Pythagoras, the era in which he lived and his proof of the Pythagorean Theorem. Choose one of the following essays to complete.

A. What factors motivated Pythagoras to develop his proof, what is now known as the Pythagorean Theorem? How do you think Pythagoras' broad interests, life experience, and beliefs influenced his scientific work? How does the mathematical advances of Pythagoras' day differ from today's mathematical research?

B. Parallel the treatment of the Pythagorean Society to similar groups of people in other times. Why do you suppose such groups are treated in this manner?

Some examples are:
Native Americans
The Salem Witch Trials
The Persecution of the Jews
The Christian Crusades

Prepare a 5 –10 minute presentation about Pythagorean Theorem. Teach the class some of the basics of what you have learned and design a quick problem for a volunteer to practice (Don’t pick a goof ball). DO NOT READ BORING PARAGRAPHS TO THE CLASS! Discuss it like you know what you are talking about! Use several visual aids to help the class understand the topic.

Resources

Proofs

James A. Garfield - Twentieth President of the United States

Chinese Mathematics Timeline

Evaluation

Web Quest Evaluation Rubric

Conclusion

Through this project you will gain a better appreciation for the mathematicians and the mathematics that they've developed for your use. You will gain insight into what it means to be a mathematician through posing your own questions and proving or disproving their validity, as well as through your attempt to develop your own proof of the Pythagorean Theorem. Your preparation to present a proof to the class will strengthen your understanding of the Pythagorean Theorem.