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Pythagoras & His Theorem

Who Was He and

What Has He Done for UsA Virtual Field Trip

ByMs. Neff

EDUC 632October 28, 2003

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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 Pythagoras?What is the Pythagorean Theorem?What can it be used for?

How can we use it today? Ramps Stairs Roofs Baseball Football

ExtensionsTeacher Pages

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Who was Pythagoras?

Click on a button to find out about Click on a button to find out about his lifehis life

Where He Lived

When He Lived

Who He Was

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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

Baseball Football

RoofsStairs

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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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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

Ground

height

Stairs

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Rise

Run

Stair Regulations

Stair information

Chapter 3, Amendment

R314.2

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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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ExtensionsIf 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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ReferencesThese 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.