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Teacher's Guide Lesson 3 The Science of Synergy An Introductory Course in Synergetics written by Kurt Przybilla Inventor of TETRA TOPS

teachers guide lesson 3 - Kid Bots...3.8 Examples: R. Buckminster Fuller 3.81 Geodesic Domes Ask the class if anyone has ever been to Disney World. Ask them if they know th spherical

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Teacher's GuideLesson 3

The Science of SynergyAn Introductory Course in Synergetics

written by Kurt Przybilla

Inventor of TETRA TOPS

Introduction to Teachers:

I developed this course to teach and explore the concepts and ideas of SYNERGETICS, the energetic geometry advanced by the revolutionary thinker R. Buckminster Fuller.

For those who are unfamiliar with Bucky, as all his friends calledhim, it is difficult to summarize his incredible life and works. Long before the rest of theworld began talking about globalization, Bucky was talking about “Spaceship Earth.”Often described as a self-taught architect, inventor, philosopher, genius and “theLeonardo DaVinci of our time,” Bucky always insisted that he was simply “an averagehuman” that who set out to discover how our universe worked.

Bucky spent his life exploring and explaining the way nature builds. Inspired by themany recurring patterns he observed in nature, he felt intuitively that there must be certain generalized principles that governed the way the universe operated. He set out to discover and employ these principles to “help make all of humanity a success.”

For the first half of his life, he was considered to be a crackpot and most people did not take him seriously. Undeterred, Bucky kept to his mission and turned out new inventions, one after the next, from his Dymaxion House, a mass producible home he developed in the 1920’s to his three-wheeled, futuristic Dymaxion Car in the 1930’s. His persistent investigations eventually led him to the development of an“energetic geometry,” which led to the discovery of the geodesic dome, the inventionthat made him famous around the world and elegantly demonstrates many of the synergetic principles he had uncovered.

In his search for “nature’s comprehensive coordinate system,” Bucky found that naturewas using spheres, not “blocks,” to build. (See Synergetics 410.00 for a more completeexplanation.) Spheres are idealized models of energy fields, so understanding howspheres relate helps to understand how nature builds. All planets, stars and atoms arespherical.

Inspired by his life and works, I was making my own models of the shapes he describedin his most comprehensive written work SYNERGETICS: Explorations in the Geometryof Thinking when I accidentally discovered that these models made excellent spinningtoys. From this discovery, TETRA TOPS™ were born.

This course and the toys are a brief introduction to the basic concepts and structures of SYNERGETICS. I hope they help you and your students begin to discover and explore some of the eternal regenerative generalized principles of SYNERGY at work in our universe.

Enjoy,

Kurt Przybilla Inventor of TETRA TOPS

© 2001 omnidirectional ideas and Duncan Toys

Notes Before We Begin

This guide is just that: a guide. The ideas are presented as I would teach them. I strongly encourageyou to modify and expand these lessons to fit your classes. Although this guide is intended for 5thand 6th graders, it can easily be used with college students since so many of these concepts are notwidely known or taught.

Bucky Spent his life teaching others about SYNERGETICS. Many of the demonstrations and concepts used in these lessons have been adapted from and inspired by his works. This work is dedicated to him and teachers everywhere.

Teacher’s Supplement and HandoutsThis guide is accompanied by a Teacher’s Supplement which contains a number of enlarged illustrations from this guide that can be photocopied and used in class to illustrate a number of the more advanced concepts.

The Teacher’s Supplement also includes handouts for each lesson. These handouts review concepts taught in the lesson and are meant to be distributed near the end of class to reinforce what the students have learned.

TETRA TOPS™Each TETRA TOPS Synergetics Science Kit comes with enough TETRA TOPS so that each studentin the class will be able to keep one top once all of the lessons are completed. You should collect thetops each day, and on the last day (Lesson 5) you will determine who gets to keep which top.

Additional MaterialsThese lessons utilize a hands on approach to learning. Building models of the structures is animportant part of every lesson. In addition to the TETRA TOPS and Trading Cards, you will needthe following additional materials:

Sticks and ConnectorsA wide variety of materials can be used to build the structural frames. I recommend round toothpicks and small Styrofoam balls (¾" work well). This inexpensive combo works very well.Styrofoam balls are available at most hobby shops and can be reused.

Other connectors that can be used include modeling clay, gumdrops or even (mini) marshmallows.Almost any stick will do, but the pointed ends of toothpicks work well with most connectors, especially the Styrofoam balls. You will need 13 connectors and 30 sticks per small group.

Flexible Joints and DowelsA number of lessons are best demonstrated with a flexible model. To build it you will need somerubber tubing and some sticks that fit inside the tubes. I suggest doweling or even pencils. The flexible CUBOCTAHEDRON you will assemble in Lesson 4 is sold as a toy. Several different versions are commercially available, so you may want to pick one up instead of making your own.

Straw ModelsVery nice models of the structures taught in these lessons can be made with stir straws and a gluegun. You will find that these models are surprisingly elegant, strong and lightweight. I recommendpre-making them for a number of lessons, and I strongly encourage you to do so. These models areinvaluable tools and are nice objects to keep around in your classroom long after you've taught thelessons.

Suggestions and CommentsI hope that you will find this guide useful for learning and teaching many of the concepts within. It is a work in progress and any shortcomings, spelling mistakes or errors are all my own. Inencourage you to send me your suggestions, comments, and feedback. Please send them to me at [email protected]

Let me take this chance to thank all of you TEACHERS. You are doing the most important job in theworld. THANK YOU!

Lesson Objective:To introduce the ICOSAHEDRON and learn about the AXES of SPIN. Familiarize them withthe Platonic Solids and R. Buckminster Fuller.

3.1 Warm Up: Axes of spin

Have a globe at the front of the class and spin it. Ask if anyone knows what it is spinning onto elicit the answer “AXIS.” Discuss how the Earth spins on a single AXIS.[You can point out the 25° angle of declination if you wish.]

Have them imagine a traditional spin top and ask how many AXES it has. Take out a traditional top and show them that is has only one AXIS.

Now hand out the OCTAHEDRON TETRA TOPS™ and ask how manyAXES of SPIN it has. Let them look at and spin them. When someone discovers the answer, have the student explain it to the class, pointing out the 3 AXES.

Draw 3 axes of spin on the board and discuss the XYZ cube-based Cartesian Coordinate system. Point out that these 3 axes relate to each other at 90°.

Now hand out the TETRAHEDRON TETRA TOPS and ask how many AXES they have.Point out that the TETRAHEDRON has more AXES though it has less balls.

TETRA TOPS are the worlds first tops with more than one axis of spin.

3.2 Review

Make another chart on the board and this time add an AXES column. Put TETRAHEDRONand OCTAHEDRON on the chart and elicit the answers to review.

3.3 Introduce the Icosahedron

Divide the class into small groups and give each an ICOSAHEDRON TETRA TOP. Tell themthat it is called an ICOSAHEDRON and ask them to figure out what “ICOSA” means. If theydon’t know where to start, remind them of what “TETRA” and “OCTA” mean using the chart.Remind them what “HEDRON” means.

At this point, students should be familiar with the concept that the Greeks named theseshapes based on the number of faces, so what you are really asking them is how many facesthere are on an ICOSAHEDRON. Tell them to imagine the internal structure. Give them sometime to work on the answer. This is not such an easy question, so don’t immediately confirmor deny any response.

3.4 Folding an Icosahedron

Materials: Tape, scissors, photocopied handout for each student

Give everyone a copy of the paper icosahedron pattern. Have them cut out, fold, and assemble the paper ICOSAHEDRON. This should take around 15 minutes.

Lesson 3: ICOSAHEDRONS AND AXES fig: 3.0

fig: 3.1

3 Axes of Spin

fig: 3.2

3.5 Compare and Discuss

When students complete the assembly encourage them to compare it to the ICOSAHEDRON TETRA TOP™.

Add ICOSAHEDRON to the chart and allow them to figure out the answers as a group. After they have had some time to work on the questions, elicit the answers.

3.6 Concept: Icosahedrons are spherical.

Teach them that the ICOSAHEDRON is the closest you can get to aSPHERE with EQUILATERAL TRIANGLES.

Have them notice the ball-like shape of both the paper models and the ICOSAHEDRAL TETRA TOP. Contrast this form to the TETRAHEDRON and the OCTAHEDRON.

3.7 Discuss: Platonic Solids

The 3 shapes that they have studied so far are commonly referred to as “Platonic Solids,”because Plato (380 B.C.) discussed them in one of his writings. He associated them with different “elements.”

The Greeks named these shapes for the number of faces and thought of them as solids. Theymade solid models out of wood and stone. Discuss how their paper models differ from theother models they have made so far.

Point out that the stick models demonstrate how the structure is not a solid and that all of thefaces are actually empty holes. Have them imagine an ICOSAHEDRON made of sticks.Optional: If time permits, have the students build an ICOSAHEDRON.

Point out that TETRA TOPS are the most basic models of these shapes & that only the VERTEXES are needed to describe or define the shape. Use chart to emphasize that number of VERTEXES is less than the number EDGES or FACES, except in the TETRAHEDRON.

3.8 Examples: R. Buckminster Fuller

3.81 Geodesic Domes

Ask the class if anyone has ever been to Disney World.Ask them if they know th spherical dome. Show thema picture of the dome and tell them its structure isbased on an ICOSAHEDRON.

Tell them that it is a GEODESIC DOME & that a very interesting man, named R. BuckminsterFuller, discovered and developed GEODESIC DOMES by studying the way nature builds.

Explain how many GEODESIC DOMES are made by breaking down the same sized triangleof an ICOSAHEDRON into triangles of different sizes. Tell them the more triangles, therounder the shape of the DOME. The FREQUENCY of a dome is determined by the number ofdivisions. [Use enlarged pictures from the Teaching Supplement to illustrate this.]

3.82 The Dymaxion™ Air-Ocean World Map

Bucky realized that because the ICOSAHEDRON was the closestshape to a sphere with equal triangles that would be the best shapeto make a map of the earth.

Point out that the MERCATOR PROJECTION that hangs in most classrooms is not accurate.

fig: 3.3

4 Frequency Dome Bucky's Expo '67 DomeMontreal Canada

fig: 3.4 fig: 3.5

fig: 3.6

Incredible visible distortion is caused by this cylindrical method of projection. The farther from the Equator, the greater the distortion, so that Greenland appears to be the same size as Africa and only the edge of Antarctica appears on a MERCATOR PROJECTION.

Point out the distortion gauge that is on a MERCATOR PROJECTION.

The Fuller Projection shows the entire Earth's surface without any visible distortion. It is themost accurate flat map of our planet. Bucky hoped his map would be used as a tool to helpthe crew of “Spaceship Earth” realize we live on “a one-world island, in a one-world ocean.”

Bucky received the first patent for cartography in the U.S. for his projection in 1946.See if the class can find the continents. Point out how they are really part of the same land mass.

Stop misinforming your students! Get your class a DYMAXION™ MAP!The Buckminster Fuller Institute (www.bfi.org) has a great selection. ORDER TODAY!I strongly recommend the very beautiful WorldSat (satellite composite) version.Also: Check the Web Guide for a beautifully animated version online.

The Dymaxion™ Map Air-Ocean World Map – The Fuller Projection is the registered copyright andtrademark of © 1938, 1967, 1980 and 1992 of the Buckminster Fuller Institute. All rights reserved.Used by permission. www.bfi.org

3.8 Examples: Nature

3.81 Viruses

These protein shells (CAPSID) protecting the genetic code of many viruses display ICOSAHEDRAL symmetry. This is one of the reasons that viruses are so tough. [See the web guide for more info about viruses and their structure.]

3.82 Bucky Balls

3.821 DISCUSS TRUNCATED ICOSAHEDRONTell them that cutting off the corners of an ICOSAHEDRON createsa familiar shape. Show them Fig. 3.8.

Ask if they can guess what it is.

3.822 BUCKMINSTERFULLERENEThe structure of Carbon-60, a third form of pure carbon (ALLOTROPE) discovered in 1985, is a TRUNCATED ICOSAHEDRON. The other two are diamond and graphite. It is on of thestrongest substances known, and is the most spherical molecule known.

Named Buckminsterfullerene, in honor of the inventor of GEODESIC DOMES, they are also called “BUCKY BALLS.” Their discovery has led to the discovery of a whole new class of CARBON molecules called FULLERNESS.

Harold Kroto, Richard Smalley, and Robert Curl, Jr. were awardedthe Nobel Prize in Chemistry for their discovery in 1996.

If you have a chemical model kit, build your own to show the class.

3.9 Conclusion

Give everyone an ICOSAHEDRON Handout and Trading Card. Allow the students a chanceto review the material on their own.

fig: 3.7

fig: 3.8

fig: 3.9

Web GuideThe internet is an incredible resource to learn more and supplement your lessons.

Here are my recommendations.

Buckminster Fuller Institute: An excellent resource for more info, books and toys. Order your class a Dymaxion™ Map here!http://www.bfi.org

A Bio of Bucky: A good, concise biography of Bucky. Nice photos.http://biosphere.ec.gc.ca/bio/bios/hist/hist_00000_a.html

Buckminster Fuller Virtual Institutehttp://www.cruzio.com/~joemoore/index.html

R. Buckminster Fuller: Thinking Out Loud: Website for PBS Special on Bucky. Very Good overview documentaryhttp://www.thirteen.org/cgi-bin/bucky-bin/bucky.cgi

Synergetics: The complete text of R. Buckminster Fuller's Synergetics. An incredible resource!http://www.rwgrayprojects.com/synergetics/synergetics.html

Synergetics on the Web: A great introduction to many of the concepts of Synergetics put together by Kirby Urner.http://www.grunch.net/synergetics

Dymaxion Map Animation: GREAT! An animation of a globe unfolding into the Dymaxion Map. CHECK IT OUT!http://www.westnet.com/~crywalt/unfold.html

Dymaxion Car: Bucky's futuristic car.http://www.washedashore.com/projects/dymax/

The World Game: A game developed by Bucky to solf the problems facing our Earth.http://www.hfmgv.org/dymaxion/index.htm

GENI: A site dedicated to Bucky's proposal for a worldwide enery grid.http://www.geni.org

Geodesic Math: A good primer.http://home.san.rr.com/wackel/Geometry/GeoSubdivision.html

The South Pole Dome: A number of sites with good pictures of the geodesic dome at the South Pole.http://ast.leeds.ac.uk/haverah/spaseman/polestat.shtmlhttp://www.glacier.rice.edu/expedition/2_usbases.amundesen.htmlhttp://astro.uchicago.edu/cara/vtour/pole/dome/

Alexander Graham Bell: Great pictures of his kites, tower, and octet truss.http://www.grunch.net/synergetics/bell.htmlhttp://www.fitzgeraldstudio.com/html/bell/inventor.html

George H. Hart's Virtual Polyhedra: INCREDIBLE! Everything you ever wanted to know about polytedra. Animated models.http://www.georgehart.com/virtual-polyhedra/vp.html

Fun Polyhedra Applet: Excellent resource of Teachers on Crystals.http://forum.swarthmore.edu/alejandre/applet.polyhedra.html

Planetary Icosahedra: Icosahedral cut outs for many different planets.http://planetscape.com/solar/eng/ico.htm

Acknowledgements

I would like to thank my parents, two of the greatest teachers I'veever known, for all of their comments, advice and wisdom. Specialthanks to Mike Burke for all of his support and patience. I would

also like to give my thanks and respect to Duncan® Toys for supporting and promoting the educational aspects of their toys.

Thanks to Lydia Bohm for proofing this. Special thanks to Lauren Darges and the Buckminster Fuller Institute.

Copyright © 2110 omnidirectional ideas and Duncan Toys

Published by Duncan® Toys CompanyP.O. Box 97 Middlefield, OH 44062

Teacher's SupplementLesson 3

The Science of SynergyStudent Handouts and Enlarged Illustrations

written by Kurt Przybilla

Inventor of TETRA TOPS

© 2001 omnidirectional ideas and Duncan Toys