Pythagorus and His Theorem - PowerPoint - PowerPoint by 0FGe9ais

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




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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!
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Pythagorean Path
Who was                      How can we use it
Pythagoras?                  today?
                                 Ramps
What is the
                             

                                Stairs
Pythagorean
                                Roofs
Theorem?                        Baseball
What can it be used             Football
for?                         Extensions
                             Teacher Pages

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Who was Pythagoras?
Click on a button to find out about his life


     Who He Was      Where He Lived



             When He Lived




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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.
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What is the Pythagorean
Theorem?

                 Pythagorean Theorem



    Proving the Theorem       Another Visual Proof




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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



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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.



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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


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




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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

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



                Ground

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Stair information

            Rise          Stair Regulations


                             Chapter 3,
                          Amendment R314.2
                               Run




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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.

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Let’s look at some roofs




            From “Wagner Rooflines – Summer 1999”
                http://www.wagnerroofing.com/


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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




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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.



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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.
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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




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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



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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.



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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.


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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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Teacher Notes
 This is designed for 8th 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.

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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, from
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.

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