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Pythagoras & His Theorem

Pythagoras & His Theorem . Who Was He and What Has He Done for Us A Virtual Field Trip. Adapted from Ms. Neff. Directions to follow the Pythagorean Path. Use the worksheet to guide you with the tasks you need to complete. Field Trip Guide

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Pythagoras & His Theorem

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

  2. Directions to follow the Pythagorean Path • Use the worksheet to guide you with the tasks you need to complete. Field Trip Guide • 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? How can we use it today? Pythagorean Path • What is the Pythagorean Theorem? • What can it be used for? • Ramps • Stairs • Roofs • Baseball • Football • Extensions

  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? Pythagorean Theorem More Visual Proofs 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-life 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. 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. Stairs door height Ground

  13. Stair information Stair Regulations Rise Run

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

  16. 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. 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. 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. 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. 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 Field Information

  21. 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. 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. 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 • 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 • To learn more about other ballparks, go to http://www.ballparks.com/baseball • To solve more Pythagorean theorem problems, go to http://www.pbs.org/wgbh/nova/proof/puzzle

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