1. Path Next Previous Pythagoras & His Theorem Who Was He and What Has He Done for Us A Virtual Field Trip By Ms. Neff EDUC 632 October 28, 2003

2. Path Next Previous Directions to follow the Pythagorean Path Use the worksheet to guide you with the tasks you need to complete. If you click on the Path button, you will be able to jump anywhere in the field trip. The Next button takes you to the next page in the sequence. The Previous button takes you back to the last page you were at. If you go to a website, close the window or click the back button from the website to return to the field trip. Enjoy your trip along the Pythagorean Path!

3. Path Next Previous Pythagorean Path Who was Pythagoras? What is the Pythagorean Theorem? What can it be used for? How can we use it today? Ramps Stairs Roofs Baseball Football Extensions Teacher Pages

4. Path Next Previous Who was Pythagoras? Click on a button to find out about his life Where He Lived Where He Lived When He Lived When He Lived Who He Was Who He Was

5. Path Next Previous The Pythagorean Theorem The Pythagorean Theorem is one of the most well-known mathematical theorems. It has been proven by many different methods and entire books have been devoted to investigating its properties. Pythagoras is thought to be the first person to actually prove the theorem, although the Babylonians are believed to have discovered it about 1000 years before Pythagoras.

6. Path Next Previous What is the Pythagorean Theorem? Pythagorean Theorem Proving the Theorem Another Visual Proof

7. Path Next Previous What can it be used for? Find the hypotenuse of a right triangle Find a missing leg of a right triangle Determine if a triangle is a right triangle

8. Path Next Previous How can we use this theorem today? If there is a right triangle, the Pythagorean Theorem can be used. There are many real applications of right triangles. Let’s look at some of these uses.

9. Path Next Previous Some real ideas Click on a button to find out how the Pythagorean Theorem is used for each of these things. Ramps BaseballFootball RoofsStairs

10. Path Next Previous Ramps Ramps for buildings are actually right triangles. Read about the regulations that are required for accessibility Code for Ramps

11. Path Next Previous Let’s see how this would work We know the amount of incline that is allowed, the rise. We know the amount of distance required to cover, the run. We can calculate the ramp distance needed to accommodate these dimensions. a 2 + b 2 = c 2

12. Path Next Previous Staircases are basically right triangles. If you know how far a door is from the ground, you can find out how far your steps will need to come out from the wall. door Ground height Stairs

13. Path Next Previous Rise Run Stair Regulations Stair Regulations Stair information Chapter 3, Amendment R314.2

14. Path Next Previous Another use - Roofs Roofs also use the Pythagorean Theorem. They usually have a pitch (or slope) and can use the theorem to determine how much material will be needed to complete a roof project. This is important as this is a large expense for many homeowners.

15. Path Next Previous Let’s look at some roofs From “Wagner Rooflines – Summer 1999” http://www.wagnerroofing.com/

16. Path Next Previous Types of roofs Look at the roof types available on many houses. Decide which one you think would take the least amount of material to build or repair. Roof Types

17. Path Next Previous Another Use – Baseball How difficult is it to hit a homerun in say – Fenway park, where they have the Green Monster in left field? Let’s check it out.

18. Path Next Previous Baseball To find out how far a baseball must be hit to clear the Green Monster in left field at Fenway Park in Boston, you can use the Pythagorean Theorem. Find out how tall the wall is and how far it is away from home plate. These measurements create a right triangle and you can find out how far a ball needs to be hit.

19. Path Next Previous Fenway Park Click on the Statistics button to find the height of the left field wall and the distance from home plate. Fenway Park Statistics

20. Path Next Previous Football Field goals are scored in football when a team kicks the football through the uprights of the goalpost. The team receives 3 points for a field goal if they are successful. Click on the Field Information button to find out about the field. Field Information

21. Path Next Previous Field Goals Now that you know how far the goalpost is off the ground, and you can find out how far the kicker is from the goal line, you can determine how far the football must be kicked to just clear the goalpost cross bar.

22. Path Next Previous Thank you for taking this tour of the Pythagorean Theorem. There are some additional sites you can go to and some other places you can go to explore other uses of the Pythagorean Theorem in the real world on the Extensions Page.

23. Path Next Previous Extensions If you are interested in learning more, go to these sites To learn more about Pythagoras, go to http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Pythagoras.html To learn more about other proofs, go to http://www.cut-the-knot.org/pythagoras/index.shtml http://www.cut-the-knot.org/pythagoras/index.shtml To learn more about ramps and accessibility at Kansas University, go to http://www.digitaljayhawk.org/kuedge/j415/415_projects/attig_h/full_story.html http://www.digitaljayhawk.org/kuedge/j415/415_projects/attig_h/full_story.html To learn more about other ballparks, go to http://www.ballparks.com/baseball http://www.ballparks.com/baseball To solve more Pythagorean theorem problems, go to http://www.pbs.org/wgbh/nova/proof/puzzle http://www.pbs.org/wgbh/nova/proof/puzzle

24. Path Next Previous Teacher Notes This is designed for 8 th grade Algebra students as an individual trip or as a classroom excursion. Students will be able to use the Pythagorean Theorem to solve real world problems. This trip should take no more than one 90-minute class period. This can be used following the introduction of the Pythagorean Theorem, as students will be completing calculations. See the Field Trip Guide worksheet provided for Algebra.Field Trip Guide

25. Path Next Previous References These are the websites that I used to complete this field trip. NOVA Online, The Pythagorean Puzzle. (2000). Retrieved October 27, 2003, from http://www.pbs.org/wgbh/nova/proof/puzzle. http://www.pbs.org/wgbh/nova/proof/puzzle O’Conner, J. J. and Robertson, E. F. (1999). Pythagoras. Retrieved October 20, 2003, from http://www-history.mcs.st- andrews.ac.uk/history/Mathematicians/Pythagoras.html http://www-history.mcs.st- andrews.ac.uk/history/Mathematicians/Pythagoras.html Realtors Monthly Online. (05/01/2001). Retrieved October 27, 2003, from http://www.realtor.org/rmodaily.nsf. http://www.realtor.org/rmodaily.nsf