# 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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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
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.
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
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

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
http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Pythagoras.html

http://www.cut-the-knot.org/pythagoras/index.shtml
Kansas University, go to
http://www.digitaljayhawk.org/kuedge/j415/415_projects/attig_h/full_story.html

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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