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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

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

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.
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

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