GeoGebra 3D & AR: Geometry Resources & Challenges

Tim Brzezinski, Sep 11, 2019

This book contains resources students can readily explore within GeoGebra 3D Calculator. Directions to explore any resource within Augmented Reality (within GeoGebra 3D Calculator app installed on any iOS or Android device) can be found at the bottom of each resource page. This volume also contains some augmented reality modeling challenges for students (last chapter). This volume is a work-in-progress and will continue to grow over time. Wishing you and your students much success in your exploratory journey of learning mathematics! -Tim B

Table of Contents

  1. Quick Intro
    1. GeoGebra 3D with AR (iOS): Quick Setup Instructions
    2. GeoGebra 3D with AR (Android): Quick Setup Instructions
    3. 3D to AR: Quick Method
  2. Geometry Resources
    1. Surface Area: Intuitive Introduction
    2. Volume: Intuitive Introduction
    3. Surface of Revolution: 3D Augmented Reality Template
    4. Diagonal Hint for a Rectangular Prism
    5. Build Your Own Right Triangular Prism (V2)!
    6. Unwrapping a Cylinder: REVAMPED!
    7. Cone Anatomy
    8. Square Pyramid: Underlying Anatomy
    9. Sphere as a LOCUS: Quick Exploration and Prompt
    10. Sphere + Plane = ?
    11. Cube: Exploration Template
    12. Tetrahedron: Exploration Template
    13. Octahedron: Exploration Template
    14. Dodecahedron: Exploration Template
    15. Icosahedron: Exploration Template
  3. Miscellaneous Resources
    1. Exploring Cross Section and Surface of Revolution Intuitively
    2. Exploring Ordered Triples
    3. Season Changes: Sun-Earth Demo
    4. 3D Abe: Silhouette = Surface of REV Cross Section
    5. Freehand Pottery Bowl Surface of Revolution
  4. AR Modeling Challenges
    1. Cone and Cylinder AR Modeling Challenge
    2. Cylinder and Hemisphere AR Modeling Challenge
    3. Toblerone Candy AR Modeling Challenge

1.

Quick Intro

  • 1. GeoGebra 3D with AR (iOS): Quick Setup Instructions
  • 2. GeoGebra 3D with AR (Android): Quick Setup Instructions
  • 3. 3D to AR: Quick Method

1.1.

GeoGebra 3D with AR (iOS): Quick Setup Instructions

WHAT TO DO:
1) Here's the link to [url=https://itunes.apple.com/us/app/geogebra-3d-graphing-calc/id1445871976]GeoGebra 3D Calculator[/url] on AppStore. Install it on your iOS device. [br][br]2) Once it's installed, open the app. Use the app to create any 3D solid. [br] Here, we simply created a sphere by using the SPHERE WITH CENTER THROUGH POINT [icon]https://www.geogebra.org/images/ggb/toolbar/mode_sphere2.png[/icon] tool. [br] (This tool is the 5th one in on the left on the top row in the pic below). [br]
3) Next, press the [b]AR [/b]button (lower right within 3D Graphics pane). You'll see everything disappear and you'll see your environment on the screen. Move your device slowly, making sure to AIM IT AT THE FLOOR. Wait a few seconds. Look for a SQUARE to appear. Once you see it, touch anywhere on the screen to place the object in your environment. [br][br]Use your fingers to reposition the objects. KEY IS TO MOVE SLOWLY. [br][b][color=#1e84cc]Have fun exploring! [br][br][/color][/b]4) Press the 3D button (lower right) to exit AR view.
Quick (Silent) Demo (done on iPad)
Quick (Silent) Demo (done on iPhone)
– Tim Brzezinski

1.2.

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2.

Geometry Resources

  • 1. Surface Area: Intuitive Introduction
  • 2. Volume: Intuitive Introduction
  • 3. Surface of Revolution: 3D Augmented Reality Template
  • 4. Diagonal Hint for a Rectangular Prism
  • 5. Build Your Own Right Triangular Prism (V2)!
  • 6. Unwrapping a Cylinder: REVAMPED!
  • 7. Cone Anatomy
  • 8. Square Pyramid: Underlying Anatomy
  • 9. Sphere as a LOCUS: Quick Exploration and Prompt
  • 10. Sphere + Plane = ?
  • 11. Cube: Exploration Template
  • 12. Tetrahedron: Exploration Template
  • 13. Octahedron: Exploration Template
  • 14. Dodecahedron: Exploration Template
  • 15. Icosahedron: Exploration Template

2.1.

Surface Area: Intuitive Introduction

TEACHERS:
For an introductory class activity related to this, [url=https://www.geogebra.org/m/mgwejudc]click here[/url].
– Tim Brzezinski

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2.4.

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2.5.

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2.6.

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2.7.

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2.8.

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2.9.

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2.10.

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2.11.

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2.12.

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2.13.

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2.14.

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2.15.

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3.

Miscellaneous Resources

  • 1. Exploring Cross Section and Surface of Revolution Intuitively
  • 2. Exploring Ordered Triples
  • 3. Season Changes: Sun-Earth Demo
  • 4. 3D Abe: Silhouette = Surface of REV Cross Section
  • 5. Freehand Pottery Bowl Surface of Revolution

3.1.

Exploring Cross Section and Surface of Revolution Intuitively

Math Teachers:
In this resource, we'll learn how to use GeoGebra's [b]Freehand Shape tool[/b] [icon]/images/ggb/toolbar/mode_freehandshape.png[/icon] to quickly sketch (to the best of our ability) a cross section of the pottery bowl shown below. [br][br]We'll then spin this sketch fully about the xAxis to create a 3D surface of revolution. [br][br]After this, we'll open this construction within GeoGebra 3D app on our phones and explore our construction (both cross section AND surface) in Augmented Reality.
[size=150]Here, we will sketch a cross section of this bowl and rotate it fully about the xAxis. [/size]
HOW TO DO IT (in less than 12 minutes)
Here is what the graph in the video looks like.
TO EXPLORE THE RESOURCE ABOVE IN AUGMENTED REALITY:
1) Open up GeoGebra 3D app on your device. [br][br]2) Press on the 3 horizontal bars (upper left). Select OPEN or SEARCH. [br][br]3) In the search bar, type [b]aavgbgnt[/b][br] Note these characters are the last 8 characters in the URL to this resource. [br][br]4) Get the cross section and bowl in a good view (zoom out if you need to). [br][br]5) Press the AR button (lower right) and go from there!
Quick (Silent) Demo
– Tim Brzezinski

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4.

AR Modeling Challenges

This chapter contains some GeoGebra 3D Calculator Augmented Reality modeling challenges. The purpose of such a challenge is for students to use GeoGebra 3D to mathematically construct (model) the real solids shown here. And Augmented Reality empowers students to test the accuracy of their models by using their phone or tablet to superimpose the virtual models they build over the real ones -- right in their environment. Have fun with these!

  • 1. Cone and Cylinder AR Modeling Challenge
  • 2. Cylinder and Hemisphere AR Modeling Challenge
  • 3. Toblerone Candy AR Modeling Challenge

4.1.

Cone and Cylinder AR Modeling Challenge

In the screencast below, both the cylinder and cone have equal radii and equal heights. [br]The height of each is double the radius. [br]Their circular bases are tangent to each other. [br][br]How can we construct this 3d image in GeoGebra 3D Graphing Calculator on your device? [br]Try to do so, and then project what you create in Augmented Reality. [br][br]If you're up for it, you can find such solids or create them from cardstock and put them to the "AR TEST" as shown in the screencast below. [br][br][b][color=#1e84cc]How well do the virtual images place when superimposed on top of the real world objects? [/color][/b]
Quick Demo
– Tim Brzezinski

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Information