Pythagorean theorem vft

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Virtual Field Trip for Pythagorean Thm

Transcript of Pythagorean theorem vft

  • 1. Pythagoras & His Theorem Who Was HeandWhat Has He Done for Us A Virtual Field Trip By Ms. Neff EDUC 632 October 28, 2003

2. Directions to follow thePythagorean Path

  • Use the worksheet to guide you with the tasks you need to complete.
  • If you click on thePathbutton, you will be able to jump anywhere in the field trip.
  • TheNextbutton takes you to the next page in the sequence.
  • ThePreviousbutton takes you back to the last page you were at.
  • If you go to a website, close the window or click thebackbutton from the website to return to the field trip.
  • Enjoy your trip along the Pythagorean Path!

3. 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. Who was Pythagoras?

  • Click on a button to find out about his life

Where He Lived When He Lived Who He Was 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.
  • Lets 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 Baseball Football Roofs Stairs 10. Ramps

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

Code for Ramps 11. Lets 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.

  • Staircases are basically right triangles.If you know how far a door is fromthe ground, you can find outhow far your steps willneed to come outfrom the wall.

Stairs door Ground height 13. Stair information Rise Run Stair Regulations Chapter 3, Amendment R314.2 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. Lets look at some roofs From Wagner Rooflines Summer 1999http://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. AnotherUse Baseball

  • How difficult is it to hit a homerun in say Fenway park, where they have the Green Monster in left field?
  • Lets 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 field goal if they are successful.
  • Click on theField Informationbutton to find out about the field.

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 tohttp://www.cut-the-knot.org/pythagoras/index.shtml
    • To learn more about ramps and accessibility at Kansas University, go tohttp://www.digitaljayhawk.org/kuedge/j415/415_projects/attig_h/full_story.html
    • To learn more about other ballparks, go tohttp://www.ballparks.com/baseball
    • To solve more Pythagorean theorem problems, go tohttp://www.pbs.org/wgbh/nova/proof/puzzle

24. Teacher Notes

  • This is designed for 8 thgrade 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 theField Trip Guideworksheet provided for Algebra.

25. References

  • These are the websites that I used to complete this field trip.
  • NOVA Online, The Pythagorean Puzzle.(2000). Retrieved October 27, 2003, fromhttp://www.pbs.org/wgbh/nova/proof/puzzle .
  • OConner, 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
  • Realtors Monthly Online . (05/01/2001). Retrieved October 27, 2003, fromhttp://www.realtor.org/rmodaily.nsf.