3D Solids
Contains 3D Solids for exploration, discovery, and application.
Table of Contents
- Basic Solids
- Rectangular Prism: Anatomy Exploration
- Triangular Prism: Anatomy Exploration
- Build Your Own Right Triangular Prism!
- Right Triangular Prism!
- Adjustable Triangular Prism
- Square Pyramid: Underlying Anatomy
- Unwrapping a Cylinder
- Unwrapping a Cylinder: REVAMPED!
- Unwrapping a cone v2
- Diagonal Hint for a Rectangular Prism
- Sphere Investigation
- Composite Solids
- Silo
- Pyramid on Rectangular Prism
- Mailbox? Backpack? (Composite Solid)
- Washer Action!!! (1)
- Platonic Solids
- 3 Golden Rectangles Surprise!
- Dodecahedral Surprise!
- 3D Transformational Geometry
- Reflection About a Plane
- Quadric Surfaces
- Circular Paraboloid of Revolution
- Special Spheroid Action: Locus Illustration
- Special Hyperboloid of 1 Sheet as a Locus
- Special Hyperboloid of 2 Sheets as a Locus
- Shortest Path Between 2 Points on a Sphere
- Other Surfaces
- Holiday Fun!
- Holiday Fun (2)!
- Catenoid
- Figure 8 Immersion of the Klein Bottle
Rectangular Prism: Anatomy Exploration
BIG POINT is moveable.
Silo
BIG WHITE POINTS are moveable.
3 Golden Rectangles Surprise!
Creation of this applet was inspired by a [url=https://twitter.com/pickover/status/902195365407059969]tweet[/url] from [url=https://twitter.com/pickover]Cliff Pickover[/url]. [br][br]Slide the slider [b]very slowly[/b]. [br][br][b]Enjoy! [br][br][color=#1e84cc]To explore in Augmented Reality[/color][color=#1e84cc], see the directions below the applet. [/color][/b]
TO EXPLORE IN AUGMENTED REALITY:
1) Open up GeoGebra 3D app on your device.[br][br]2) Go to MENU (upper left corner). [br] Go to OPEN. Under [b]Search[/b], type [b]YGu6kVpR[/b]. [br] Find the slider named [b]b[/b] and slide it slowly.
Reflection About a Plane
In the applet below, the [b][color=#bf9000]yellow triangular pyramid[/color][/b] (with [b][color=#ff00ff]LARGE PINK VERTICES[/color][/b]) has been reflected about the [b][color=#999999]gray plane[/color][/b]. [br][br]You can alter the appearance of the [b][color=#bf9000]yellow pyramid (pre-image)[/color][/b] at any time by moving any one (or more) of the [b][color=#ff00ff]LARGE PINK VERTICES[/color][/b]. [br][br]You can change the orientation of the [b][color=#999999]plane[/color][/b] by moving any one (or more) of the [b][color=#ff7700]3 ORANGE POINTS[/color][/b] it passes through. [br][br][b]Explore! [/b][br][br]Be sure to answer the question that follows.
1.
Suppose you stand 4 ft away from a mirror. How far would your image be away from the glass (assuming you could "reach in" and measure)? How is your conclusion somewhat supported by any dynamics you see here?
Quick (Silent) Demo
Circular Paraboloid of Revolution
[color=#000000]Recall the locus definition of a [b]parabola[/b] (illustrated [url=https://www.geogebra.org/m/BFK6P7Ac]here[/url] if you need a refresher). [br][br]Well, imagine spinning this parabola 360 degrees about its axis (of symmetry).[br]Doing so yields a 3D solid called a [/color][b][color=#bf9000]circular paraboloid of revolution. [br][br][/color][/b][color=#000000]Interact with this applet for a few minutes.[/color] [br][color=#cc0000][i]Be sure to slide the[/i][/color] [b][color=#000000]Slide Me![/color] [/b][color=#cc0000]slider completely once [/color][b][color=#000000][i]before[/i][/color][/b][color=#cc0000] messing around with the other sliders! [br][/color][color=#1e84cc][b]Note: Point P is a point that lies on this solid. Move it wherever you'd like. [br] [/b][/color]After doing so, answer the question that follows. [br][br][color=#1e84cc][b]To explore this resource in Augmented Reality, see the directions that appear below the applet. [/b][br][/color]
A circular paraboloid of revolution is a locus (set of points that satisfy a condition or set of conditions). [br]How would you describe this locus?
To Explore in Augmented Reality:
1) Open up GeoGebra 3D app on your device.[br][br]2) Go to MENU, OPEN. Under SEARCH, type [b]g3uusvay[/b][color=rgba(0, 0, 0, 0.870588235294118)].[br][br][/color]3) [b]The xcoord slider controls the x-coordinate of point P. [br] The ycoord slider controls the y-coordinate of point P.[/b][b][color=#bf9000] [br] The yellow e slider controls the opacity of the paraboloid.[br][/color][/b][b][color=#0000ff] The blue i slider controls the opacity of the (directrix) plane.[br][/color][/b][b] The a slider stretches (or compresses) the paraboloid vertically (with respect to z). [br] [br][/b][b] The slider named d provides the animation. [br][br][/b][b] Set the boolean variable [/b][b]n equal to "true" if you want to see [br] the 2d-parabola [/b][b]= cross section of the paraboloid of revolution and vertical plane containing P. [br][/b]
Holiday Fun!
[i]Enjoy! [br][br][/i][b][color=#1e84cc]To explore this resource in Augmented Reality, see the directions below this applet. [/color][/b]
TO EXPLORE IN GEOGEBRA AUGMENTED REALITY:
1) Open up GeoGebra 3D app on your device. [br][br]2) Go to MENU, OPEN. Under SEARCH, type the resource id (in URL above): [b]hWD7GPGB[/b][br][br]3) The four sliders to control this animation are at the top of the algebra view.