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Pythagoras

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Title: Pythagorus and His Theorem Author: Jane Neff Last modified by: Authorized User Created Date: 10/15/2003 1:36:31 AM Document presentation format – PowerPoint PPT presentation

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Title: Pythagoras


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
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

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?
Pythagorean Theorem
Proving the Theorem
  • More Visual Proofs

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-life ideas
  • Click on a button to find out how the Pythagorean
    Theorem is used for each of these things.

Ramps
Roofs
Stairs
Baseball
Football
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.
  • a2 b2 c2

12
Stairs
  • 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.

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
Lets 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?
  • 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 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/M
    athematicians/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.digitaljayh
    awk.org/kuedge/j415/415_projects/attig_h/full_stor
    y.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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