Pythagoras and the Pythagorean Theorem

Task #1

Use the following websites to answer these questions pertaining to Pythagoras.

1. What country was Pythagoras from?
2. What was the name of the secret society that Pythagoras founded?
3. True or False - Pythagoras was a vegetarian but wisdom trivia says that he sacrificed about 100 oxen because he was happy about discovering what has come to be known as his theorem
4. What kind of numbers did the Pythagorean Theorem lead the Pythagoreans to discover?
5. What is it said they did to the person who dared mention the existance of these numbers to the public?

http://www.geom.uiuc.edu/~demo5337/Group3/hist.html

6. Pythagoras studied ______ and _______ numbers, triangular numbers, and perfect numbers. Pythagoreans contributed to our understanding of __________, ____________, areas, proportion, ____________, and polyhedra.

http://www.mathopenref.com/pythagoras.html


Task #2

Use the following websites to answer the following questions and to explain in detail the Pythagorean Theorem.

1. What kind of triangles satisfy the Pythagorean Theorem?
2. What is the name of the side opposite the right angle?
3. What does the Pythagorean Theorem state?

http://www.mathsisfun.com/pythagoras.html

http://math.about.com/od/pythagorean/ss/pythag.htm


Task #3

Investigate the proofs on the following website and then draw a diagram and write an explanation of the proof in your own words.

http://www.mathsnet.net/dynamic/pythagoras/index.html

At this website, choose Proofs, then dissection proofs, explore proofs 1 through 4. After looking at the 4 proofs, choose one to draw and explain in your own words.

Here is another website with proofs in case you want to check it out too.

http://www.pbs.org/wgbh/nova/proof/puzzle/theorem.html


Task #4

Read the following website. Can you define what a Pythagorean Triple means?

http://www.saltire.com/applets/pythag/incircle.html

The website states that smallest Pythagorean Triple is [3,4,5].
Here are some more Pythagorean triples: [6, 8, 10] [9, 12, 15] [12, 16, 20] [15, 20, 25]

Can you see how we created these? Can you create the next triple in the sequence? Explain your process for creating the next triple.

Here is another sequence of Pythagorean triples:  [5, 12, 13] , [7, 24, 25] , [9, 40, 41] , [11, 60, 61]

Can you see how we created these? Can you create the next triple in the sequence? Explain your process for creating the next triple.

If you cannot create the next triple in the sequence, then go to the following website and follow the directions to create a Pythagorean Triple.

http://www.mathsnet.net/dynamic/pythagoras/index.html

At this website, choose Related things, then Pythagorean triples, this will help you find additional pythagorean triples to list. 


Task 5

List 4 things you learned today and explain why you think they are important. Please use complete sentences.


http://www.mathsisfun.com/square-root.html  - Information on Squares and Square Roots