COORDINATE SYSTEMS

Introduction

As you know, coordinates are points along a set of axes. Rene Descartes (1596-1650) was a French philosopher who figured out how coordinates could be used to locate objects. Initially, he established the X and Y axes used for a flat surface. His Cartesian coordinate system is used for rectangular spaces, such as the area of a CAD drawing. Others later added the Z axis to include the third dimension.

Descartes’s system was so helpful that people soon developed coordinate systems that could be used to locate objects within spaces having other shapes. Using coordinates is how astronomers, for example, locate stars and other celestial objects within the domed area of the night sky. Did you know that robots can be classified based on the shape of the space within which they move? A robot with a cylindrical configuration moves within a space shaped like a cylinder. What do you suppose is the shape of the space used by a robot with a Cartesian configuration?

Coordinates have long been used by explorers and other travelers. You may have used a coordinate system to locate towns on a map. If you looked in the map’s index, you found that the locations were indicated by a letter and number combination. The letter and number corresponded to letters along one axis of the map and numbers along another. The town was located where the two axes crossed. The Global Positioning System, a series of satellites orbiting the earth, uses coordinates to map the earth’s surface. If you have a GPS device, the system can also tell you exactly where you are at any time. GPS technology has become popular with mountain climbers, hikers, and treasure hunters. Can you think of other ways in which coordinates might be used?

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Task

For this WebQuest, your job is to learn more about ways in which coordinate systems are used. To demonstrate what you have learned, you will answer the questions included here. You will also complete one of the activities described at the end of this WebQuest.

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Process

Read through the following questions. Then research the Internet resources that are provided for you. As you explore the sites, look for answers to the questions. Keep a record of any sites where you find answers by noting the title and URL (Internet address). For example:

            (title) Technology Student Association
            (URL) http://www.tsaweb.org

1. What did a housefly have to do with Descartes’s coordinate system?
   
   
2. What did Descartes fail to do that caused him to publish hypotheses that included errors?
   
   
3. What is the shape of the work area required by a robot with a Cartesian configuration?
   
   
4. Geographic coordinates give the ability to locate points on the earth. At what longitude is the prime meridian located?
   
   
5. Why would mapping the surface of the earth be more difficult than mapping the surface of an equally large billiard ball?
   
   
6. Which coordinate system is used by astronomers to locate objects in outer space?

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Resources

Visit the Web sites listed here to find information that will enable you to answer the questions. You may use additional sites if you wish. Be sure to keep a record of any sites you use.

• Cartesian Coordinate System provides a general discussion of how the system was developed. Includes games.

• Coordinates and Similar Figures provides basic information about using coordinates to locate points.

• René Descartes Meet the man who developed the Cartesian coordinate system.

• Cartesian Coordinate System features drawings to simplify the subject.

• Coordinate Systems Overview explains several systems.

• Spatial Coordinate Systems discusses systems used to develop maps and globes.

• Types of Robots describes the different types and includes links to drawings showing the axes used to control their movement.

• Latitude and Longitude explains geographic coordinates.

• General Coordinate Systems includes information about the coordinate system used by astronomers.

• Geocaching is an article about one family’s quest to find hidden objects using GPS technology.

• Geocaching is the official site for this sport.

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Activities

Two activities are described below. Complete one of these activities (your choice) to demonstrate understandings you’ve gained by going on this WebQuest.

• Create a crossword puzzle that uses coordinates to establish the location where the word must be written. For example, instead of 1 across, 4 down, you might use 14, -6. Remember, the x axis is always given first.
• Locate five towns on a map. Write down their names and the map coordinates given in the index. Trade lists with a classmate and find the towns given on each other’s lists. Label the towns on the map with a sticky note or circle them with a marker.
• If a GPS device is available to you, see if a geocaching adventure is occurring in your area and take part in it. Report on your experience to the class. You might also help organize a similar activity in which the entire class could participate.

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