Pythagoras & His Theorem

1. Pythagoras & His Theorem Who Was He and What Has He Done for Us A Virtual Field Trip

2. 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. 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 Pythagorean Path

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

5. 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. What is the Pythagorean Theorem? Another Visual Proof Pythagorean Theorem Proving the Theorem

7. 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. 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. Some real ideas • Click on a button to find out how the Pythagorean Theorem is used for each of these things. Ramps Stairs Roofs Baseball Football

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

11. 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. • a2 + b2 = c2

12. 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.

13. 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.

14. 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

15. 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 fieldgoal if they are successful. • Click on the Field Information button to find out about the field. Field Information

16. 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.

17. 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. • O’Conner, J. J. and Robertson, E. F. (1999). Pythagoras. Retrieved October 20, 2003,fromhttp://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.