Augmented Reality: Ideas for Student Explorations
4 cheng
Table of Contents
- Getting Started
- Getting Started with GeoGebra Augmented Reality
- Ideas for Student Explorations & Activities
- Conic Section Explorations
- Rotating about X-AXIS: Creating Surfaces of Revolution in GGB AR
- Rotating about Y-AXIS: Creating Surfaces of Revolution in GGB AR
- Gabriel's Horn: Virtual Exploration in GeoGebra Augmented Reality
- Modeling with GeoGebra Augmented Reality: Project Ideas
- Modeling Every-Day, 3D Objects
- How to Create Surfaces of Revolution in GeoGebra Augmented Reality
- GeoGebra Augmented Reality: Modeling a Straw (Cylinder)
- GeoGebra Augmented Reality: Modeling a Fish
- GeoGebra Augmented Reality: Building Cookie Models!
- GeoGebra Augmented Reality: Modeling a Bagel
- GeoGebra Augmented Reality: Egg Modeling
- GeoGebra Augmented Reality: STEP SURFACE!
- GeoGebra Augmented Reality: Modeling Pottery and Plastic Cups
- GeoGebra Augmented Reality: Modeling a Bowling Pin
- GeoGebra Augmented Reality: Modeling a 2-Piece Lampshade
- Quick Illustrations
- Basic solids
- Penrose triangle
- Sierpinski pyramid
- Football
- Klein Bottle
- Ruled Surface
Getting Started with GeoGebra Augmented Reality
Quick (Silent) Demo
Getting Started:
Be sure to download GeoGebra Augmented Reality on your device first. [br][br][url=https://itunes.apple.com/app/geogebra-augmented-reality/id1276964610&utm_source=Download+page&utm_medium=Website&utm_campaign=GeoGebra+Augmented+Reality+for+iOS][b][color=#1e84cc]Link to GeoGebra Augmented Reality app from App Store[/color][/b][/url][color=#1e84cc]. [br][/color]
Directions:
1) Open up [b][color=#1e84cc]GeoGebra Augmented Reality[/color][/b] app on iPad or iPhone. [br][br]2) Go to MENU. Select "[b]Two Functions[/b]". [br][br]3) Delete the first equation (provided). For blue (top) equation, enter [math]z=\sqrt{9-x^2-y^2}[/math]. For bottom equation, type in [math]z=-\sqrt{9-x^2-y^2}[/math]. [br][br]4) Take a ball (sphere) and show how this is a perfect model for such a sphere. [color=#ff0000]See 0:12 - 0:15 in video.[/color] [br][br]5) Delete bottom equation (pink). Change top (blue) equation to [math]z=\sqrt{4x^2+4y^2}[/math]. (See 0:30 in video). This creates a cone. [color=#ff0000]If you have a funnel, you can show what you see in video from 0:44 to 0:54. [/color][br][br]6) Enter new pink equation z = 3. This illustrates one of the four main conic section types: A CIRCLE. [color=#ff0000]See 1:02 to 1:13 in video.[/color] [br][br]7) Now change pink equation to z = 2x + 1. This will create a cross section (intersection) that is a PARABOLA (2nd type of conic section). [color=#ff0000]See 1:16 - 1:31 in video. [br][/color][br]8) Now change pink equation to z = 0.5x + 3. This will create a cross section (intersection) that is an ELLIPSE (3rd type of conic section). [color=#ff0000]See 1:32 to 1:44 in video. [/color][br][br]9) Now change pink equation to z = 5x + 2. This will create a cross section (intersection) that is a HYPERBOLA (4th type of conic section). [color=#ff0000]See 1:45 to END in video. [/color][br][br]
Conic Section Explorations
Before we explore conic section types in GeoGebra Augmented Reality, let's explore them first in GeoGebra 3D Graphing Calculator app!
1.
[b][color=#ff00ff]Note the equation of the plane is z = some constant. [br][br][/color][/b][color=#ff00ff]Change the equation of this pink plane to z = 2. Then change it to z = 1. Then change it to z = 4. [/color][br][br]How would you describe the intersection of this [b][color=#ff00ff]plane[/color][/b] and [b][color=#1e84cc]cone[/color][/b]?
2.
Change the [b][color=#ff00ff]equation of the plane[/color][/b] to [math]z=x+1[/math]. How would you describe the intersection of this [b][color=#ff00ff]plane[/color][/b] and [b][color=#1e84cc]cone[/color][/b] now?
3.
Now change the [b]equation of the plane [/b]to [math]z=0.5x+2.5[/math]. How would you describe the intersection of this [b][color=#ff00ff]plane[/color][/b] and [b][color=#1e84cc]cone[/color][/b] now?
4.
Change the [b][color=#ff00ff]equation of the plane[/color][/b] to [math]z=3x+1.5[/math]. How would you describe the intersection of this [b][color=#ff00ff]plane[/color][/b] and [b][color=#1e84cc]cone[/color][/b] now?
Now let's explore these conic sections in GeoGebra Augmented Reality! (Silent "how-to" screencast)
Also: Quick Summary of All Conic Section Types & How They're Formed
How to Create Surfaces of Revolution in GeoGebra Augmented Reality
Here's a quick demo of a virtual model of a bowl.
How to author the 2 surface equations (z = ) to Create a Surface of Revolution in GeoGebra Augmented Reality
Basic solids
Can you find all solids that:[br]a) are pyramids?[br]b) are prisms?[br]c) consist of only triangles?[br]d) consist of only squares?[br]e) have six faces?[br]f) have twelve edges?