The history of the Pythagorean theorem and it's proofs

Introduction

Objective:

The primary purpose of this WebQuest is to teach students how to prove the Pythagorean Theorem. The secondary purpose is for them to learn it's history and use around the world.

Introduction:

The Pythagorean Theorem is one of the most well known and most used Theorems in all of mathematics. The Theorem simply states that "the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the legs". The Pythagorean Theorem is commonly displayed as......

a2 + b2 = c2

We have already discussed in class the primary ways the Pythagorean Theorem is used in solving geometrical problems. In this assignment, you are going to take an indepth look at how the Theorem came to be. You see, many historians believe that this Theorem was actually proven by the Egyptians, Chinese, and Babylonians up to 2,000 years before Pythagoras was even born. So why does Pythagoras get the credit for proving the Theorem? Pythagoras devoted many years of his life generalizing it and making it popular to the public even though he probably wasn't the first to discover it.

Each student will also be expected to direct the class through a Proof of the Theorem on the chalkboard.

There are literally hundreds of geometric and algebraic demonstrations on why the Theorem works. Even former president Garfield submitted his own Proof of the Pythagorean Theorem.

Task

The goal of this assignment is for each student to gain knowledge about the history behind the Pythagorean Theroem and some knowledge about the many ways mathematicians have proved its exsistence. This knowledge will be obtained through the Internet using the Websites provided.

The student will be expected to prove the Pythagorean Theroem on the chalkboard in front of the class as well as turn in a brief written summary of the proof and some history behind it. A worksheet compiled of sample problems using the Pythagorean Theroem will also be given to each student to solve.

Process

To be able to complete this assignment, you must gain knowledge about the history of the Pythagorean Theroem. Also, each of you will demonstrate proof of the Theroem in front of the class. Don't worry, I don't expect you to invent your own proof, but in accordance with California's Academic Standards you will recite a prior-known proof. The Websites below have been provided for you to use in accomplishing your task.

http://ualr.edu/lasmoller/pythag.htmlhttp://mathforum.org/isaac/problems/pythagthm.html http://www.arcytech.org/java/pythagoras/history.html

Evaluation

Approching 10	Accomplished 15	Advance 20	Score
WrittenPaper	Student provides a paper which shows little or no understanding of the Theorem. The paper has many grammatical and mathematical errors.	Student provides a well written paper which shows some understanding of the Theorem. The paper has several gramatical and mathematical errors.	Student provides an excellent paper which shows an exemplary understanding of the Theorem. The paper has few gramatical and mathematical errors.
Presentation to the Class	Student's mathematical techniques are unsatisfactory and provides little to no explanation.	Student uses good mathematical techniques and supports them with some explanation.	Student uses excellent mathematical techniques and supports them with clear, concise explanation.
Example Problems Worksheet	Student answers questions with less than 70% accuracy.	Student answers questions with 70%-89% accuracy.	Student answers questions with 90% - 100 % accuracy.

Approching

10

Accomplished

15

Advance

20

Score

WrittenPaper

Student provides a paper which shows little or no understanding of the Theorem. The paper has many grammatical and mathematical errors.

Student provides a well written paper which shows some understanding of the Theorem. The paper has several gramatical and mathematical errors.

Student provides an excellent paper which shows an exemplary understanding of the Theorem. The paper has few gramatical and mathematical errors.

Presentation to the Class

Student's mathematical techniques are unsatisfactory and provides little to no explanation.

Student uses good mathematical techniques and supports them with some explanation.

Student uses excellent mathematical techniques and supports them with clear, concise explanation.

Example Problems Worksheet

Student answers questions with less than 70% accuracy.

Student answers questions with 70%-89% accuracy.

Student answers questions with 90% - 100 % accuracy.

Conclusion

The Pythagorean Theorem is one of the most famous and fundamental mathematical concepts in history. You, as a student, will use this formula countless times throughout your academic career. Every time you see a right triangle in this course, or a unit circle in pre-calculus, or vectors in calculus, you will have the Pythagorean Theorem at your side ready to be applied to any or all of the right triangles you encounter.

Credits

Creator: Kinjal Shah

http://ualr.edu/lasmoller/pythag.html

Teacher Page

by Kinjal Shah

The primary purpose of this WebQuest is to teach students how to prove the Pythagorean Theorem. The secondary purpose is for them to learn it's history and use of it in different cultures around the world.

Teacher Introduction

According to California Academic Standard 8.G.B.7 for geometry, each student is to be able to "Prove and use the Pythagorean Theorem". In my experience, many of the textbooks that students use do not clearly explain the Proofs of the Pythagorean Theorem. This Webquest is intended to take the students out of the classrroom and into the computer lab to research different Proofs and the history behind the Pythagorean Theorem.