Pythagoras lived in the 500's BC, and was one of the first Greek mathematical

Pythagoras lived in the 500's BC, and was one of the first Greek mathematical

thinkers. He had a group of followers known as the Pythagoreans who followed him around and taught other people what he had taught them.

Source: http://www.historyforkids.org/learn/greeks/science/math/pythagoras.htm

Pythagoreans were interested in philosophy, but especially in music and mathematics, two ways

of making order out of chaos. Music is noise that makes sense, and mathematics is rules for

how the world works.

Source: http://www.historyforkids.org/learn/greeks/science/math/pythagoras.htm

Pythagoras himself is best known for proving that the Pythagorean Theorem was true.

Source: http://www.historyforkids.org/learn/greeks/science/math/pythagoras.htm

The Pythagorean Theorem says that in a right triangle, the sum of the squares of the two right-angle sides will always be the same as the square of the hypotenuse

(the long side). A2 + B2 = C2.

Source: http://www.historyforkids.org/learn/greeks/science/math/pythagoras.htm

A Tale of Three Cities –The Pythagorean Theorem

1. Using Google Maps, find three cities that form a right triangle. Left-click and hold the mouse to move the map to any location on the planet. Zoom in and out until the three cities fill the map window.

2. Print the map to a printer or print to a PDF creator program. Many of these programs are available for free. If you are using the PDF method, instead of saving the map as a PDF, use the PDF creator software to save the map as a JPEG (photo). Save it into a specific folder. Next, in that folder right-click on the map photo, choose copy and then open a new Presentation document where you will paste the map onto a slide.

3. On the printed map, use a straight edge to draw a right triangle between the three cities. If you are using the PDF/JPEG method, use your Presentation software to open and paste a right triangle on top of the JPEG map. You can edit the triangle using the Format Shape function (remove the fill, the thicken the line, change the line color, etc.)

4. On a separate slide, insert a Right Triangle, then add labels for the three sides and the three City Names. 5. On another slide, write out the definition for the Pythagorean Theorem (see example). 6. On the same slide, use a “Distance Finder” website to find the actual distance between the cities on side a. and

the cities on side b. of the Right Triangle (see example). 7. Use the Pythagorean Theorem to solve for the distance of side c (see example). 8. On this same slide, give the name of side c. 9. Next, solve the following problem. Traveling at an average rate of 50 miles per hour, calculate how long it will

take to make a round trip journey to all three cities, including an 8-hour sight-seeing tour in each city. Show this on a separate slide.

10. Using Custom Animation in Microsoft Powerpoint, create a presentation in which you move a vehicle around to each city on your map. Choose a vehicle using Clip Art or a photo.

11. As your vehicle reaches each city, stop and present 10 facts about that city (see list provided). Show these facts on a separate slide for each city.

Step-by-Step Instructions

A Tale of Three Cities –The Pythagorean Theorem

The first step is to go to Google Maps and use the Zoom tool to zoom in and out until you find three cities that form a right triangle.

City 1

City 2 City 3

A Tale of Three Cities –The Pythagorean Theorem

A Right Triangle placed on top of a JPEG photo of a Google Map.

Students may print the Google map to a printer and use a ruler to draw a right triangle on the map or print the map to a PDF creator program and save it as a JPEG photo. If the PDF method is used, students can copy the map into the presentation software and then insert a right triangle on top of the map as shown here using the Insert > Basic Shapes command.

a

b

c

City Name 1

City Name 2 City Name 3

A Tale of Three Cities –The Pythagorean Theorem

Students must draw a right triangle in the

presentation software with labels for the cities

and the sides of the triangle.

a

b

c

San Angelo

Dallas Galveston

A Tale of Three Cities –The Pythagorean Theorem

Example

A Tale of Three Cities –The Pythagorean Theorem

Use a Distance Finder website to find:

The distance between City 1 and City 2 (Side a.) = ___________ miles.

The distance between City 2 and City 3 (Side b.) = ___________ miles.

Using the equation for the Pythagorean Theorem, solve for the distance between City 1 and City 3 (Side c.).

232 miles2 + 269 miles 2 = c2 53,824 + 72,361 = c2 126,185 = c2

The distance between City 1 and City 3 = ____________ miles.

Side c is called the _______________________

The equation for the Pythagorean Theorem is _____________________

c2 = c 126,185 = c c = _______ miles 355

355

232

269

Example

A Tale of Three Cities –The Pythagorean Theorem

In our example, the total distance is232 miles + 269 miles + 355 miles = 856 miles

A nice little getaway.

A Tale of Three Cities –The Pythagorean Theorem

You will make a round trip journey to all three cities traveling at an average rate of 50 miles per hour. Additionally, you will stay 8 hours in each city on sightseeing tours. How long will the trip take?

_________ hours.

Solve this problem.

Distance = Rate x Time

d = r x t

856 miles = 50 miles per hour x t

856 miles = 50 miles per hour x t

50 miles per hr 50 miles per hr

t = 17 hours, then add 24 hours = 41 hours

If we know the distance (miles) and the rate (miles per hour), we can find the

time (hours) based on the following formula:

A Tale of Three Cities –The Pythagorean Theorem

Using clip art or a photo, insert a vehicle onto your map. Move it around to all three cities using Custom Animation. Stop the animation after each leg of your trip, and go to the facts for that city.

A Tale of Three Cities –The Pythagorean Theorem

FACT SHEET

City Name

1.State2.Year Founded3.Current Population4.Longitude and Latitude5.Weather Fact6.Current Mayor7.Form of Government8.Largest Employer9.Two Colleges10.A fun activity that you would do if you were there.

Find these 10 facts on each city.

Click your mouse or hit the space bar to move the car along its trip.

San Angelo

1. Texas2. 18673. 88,4394. 31°27′11″N / 100°27′9″W5. San Angelo averages 251 days of sunshine a year 6. Alvin New7. Council-manager8. Shannon Medical Center9. Angelo State University and Howard College10.10 miles of river frontage on the Concho River winding through downtown and beyond.

Dallas

1. Texas2. 18413. 1,279,9104. 32°47′0″N / 96°48′0″W5. Winters in Dallas are generally mild, with normal daytime highs ranging from 55 °F (13 °C) to 70 °F (21 °C)6. Tom Leppert7. Council-manager8. American Airlines (22,077 employees)9. Southern Methodist University (SMU) and Texas Woman’s

University10.Dallas Cowboys in the new Cowboys Stadium

Galveston

1. Texas2. The first permanent European settlements on the island were constructed around 1816 by the pirate Louis-Michel Aury3. 57,466 4. 29°18′04″N / 94°47′51″W5. In 1900, the island was struck by a devastating hurricane. It

holds the record as the United States' deadliest natural disaster killing 6,000 to 8,000 people on the island

6. Lyda Ann Thomas7. Council-manager8. University of Texas Medical Brach at Galveston9. Galveston College and Texas A&M University at Galveston10.Mardi Gras, Moody Gardens

Wow, that was a fun trip.

The End.

I hope you enjoyed this

lesson.