A Geometry Lesson in Second Life

Dean L. Zellerdzeller@cs.kent.eduDr. Paul S. Wang (advisor)Department of Computer ScienceKent State University

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About Second Life• Based on an idea within Show Crash, by Neal

Stephenson (1992).

• 13,000,000 unique accounts.

• Business conducted through Linden Dollars (US$1 L$300).

• Instant messaging and item sharing.

• Virtual meetings and classrooms.

• Is not a game.

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Lesson Objective

• The student will create geometric figures using a manipulative within the Second Life virtual world.

• Topics:– Angles– Regular polygons– Algorithms

• Requirements:– A Windows or Macintosh computer running Second

Life (found at http:// www.secondlife.com/downloads)

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Background – Bumble Bee Graphics

• You have a pet bumble bee that will move or draw as you command.

• Move Forward (mf)– Move forward without drawing– Examples: mf mf 3.0– Also: move backward (mb), move right (mr), move left (ml)

• Draw Forward (df)– Move forward drawing a line– Examples: df df 3.0– Also: move backward (mb), move right (mr), move left (ml)

• Turn Left (tl)– Make a turn to the left at the specified angle– Examples: tl 30 tl 45– Also: turn right (tr)

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Assignment 0 – Setup

• Create a Second Life account and avatar.• Become familiar with the virtual world

controls, including:– Navigation (movement and teleporting)– Communication (chat)– Inventory– Searching

• Teleport to the KSU WME Learning Land and visit the BumbleBee drawing area.

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Assignment 1 – Right Angle Figures

• Using the BumbleBee commands, complete the following tasks.

• Note that all turns will be 90 degrees.• Draw the shapes according to the diagram

specifications.• Write the code implemented on the worksheet.• All measurements are in meters.• Start and end in the same position and at the same

angle.

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Assignment 1 Tasks

• Draw a squarecode: _________________

• Draw a rectanglecode: _________________

• Draw an H-shapecode: _________________

5 m

5 m

2.5 m

5 m

1 m 1 m

5 m

2 m

2 m

3 m

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Assignment 1 Tasks, continued

• Draw an I-shapecode: _________________

• Draw an E-shapecode: _________________

• Draw an T-shapecode: _________________

1 m

1 m

5 m

2 m2 m

3 m

5 m

1 m

1 m

1 m

4 m

1 m

5 m

2 m2 m

1 m

4 m

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Assignment 1 Tasks, continued

• Draw an M-shapecode: _________________

• Challenge Question:– Draw the phrase HIT ME, separating letters by

1 m, with 3 m between the words.– Use the code from the previous tasks.

5 m

1 m1 m

4 m

1 m

1 m 1 m 1 m3 m

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Assignment 2 – Regular Polygons

• A polygon is an enclosed figure consisting of only straight lines.

• A regular polygon is a polygon in which all sides are equal length and all interior angles are equal.

Regular Polygons Irregular Polygons

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Assignment 2 Tasks

• Theorem:– The sum of the angles of a triangle is 180°. For

each additional side, add another 180°.

• Draw a regular (equilateral) triangle.– Question: The interior angle of a regular

triangle is 60 degrees (180 divided by 3). What is the angle the Bumblebee would turn to create the interior angle? ________________

– Code: _____________________

5 m

60º

60º

60º

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Assignment 2 Tasks

• Draw a regular pentagon.– Question: What is the interior

angle of a pentagon? _________– What is the angle the Bumblebee would turn to

create the interior angle? ________________– Code: _____________________

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Assignment 2 Tasks, continued

• Draw a regular hexagon.– Question: What is the interior

angle of a hexagon? _________

– What is the angle the Bumblebee would turn to create the interior angle? _______Code: _____________________

• Draw a regular octagon.– Question: What is the interior

angle of a octagon? _________

– What is the angle the Bumblebee would turn to create the interior angle? ______

– Code: _____________________

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Assignment 2 Tasks, continued

• Challenge Question– Generalize this problem for a regular polygon

with N sides.

• New command: repeat … endrep– You can repeat commands by containing them

within a repeat / endrep command.– Example: repeat 4 df 5 tl 90 endrep draws a

square of size 5.

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Further Assignments

• Stairs

• Designs

• Prisms

• Bridges

• Polyhedrons

• Etc…

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References• Zeller, D. “The Future of Internet-Based Education

through Virtual Worlds.” The International Journal of Learning, Volume 15, Issue 10, pp.45-56.

• Weber, A., Rufer-Bach, K., Platel, R. Creating your world: the official guide to advanced content creation for Second Life. 2008 Wiley Publishing, Inc. ISBN 978-0-470-17114-1.

• For other lessons in Second Life, see the WME wiki, at

http://squirrel.cs.kent.edu/wiki/index.php/Lessons

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News

• I will be presenting a Second Life workshop at the SIG-CSE conference in Chattanooga on March 3rd.

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FundingThis research is funded by the Research Center for Educational Technology (RCET) and by the Web-based Mathematics Education (WME) team at Kent State University.