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I am going to teach 3D vectors soon to my A-level students.

Last time I taught it a lot of them struggled to visualise the angle between two vectors in 3D space.

I had an idea that I could get them all 3D glasses and find some sort of immersive 3D animation of vectors.

Is there any software out there to create 3D animations (using the red and blue layers)? Or any existing videos/resources that can be viewed in 3D with the glasses?

harpomiel
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    A helpful search term: an anaglyph is a color-filtered 3D image. – Joseph O'Rourke Nov 24 '19 at 13:18
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    If the main concern is having them visualize the angle between vectors, have you checked out Calc Plot 3D? You can plot 3D vectors (use the "Add to graph" dropdown menu) and rotate the image to get a better view of the angle. This isn't an answer to your question, as it does not create anaglyphs for use with glasses. – Nick C Nov 24 '19 at 13:36
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    I would suggest obtaining some popsicle sticks. – Steven Gubkin Nov 24 '19 at 14:08
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    Paint 3D is worth a try. – Peter Saveliev Nov 24 '19 at 14:42
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    As a software engineer who does 3d geometry as part of my job, Steven Gubkin has the right idea. Some sticks and blue tack are what you need, not technology. – Sean Reid Nov 25 '19 at 15:23
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    When I was in graduate school and TA-ing for a Vector Calc course, I enlisted a friend of mine to pull a prank on the first day of class. He was a very young-looking fellow and managed to sit in the middle of the classroom and blend in like an undergrad. I began drawing on the board in red and blue chalk to make a 3D picture and said, "Ok, everyone pull out your 3D glasses!" He put his on and looked around at the others, saying, "What, you didn't bring yours?" I don't know what we expected to happen, but the silence was deafening. – Brendan W. Sullivan Nov 25 '19 at 17:11

2 Answers2

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I remembered GeoGebra doing this several years ago, but I thought that functionality died with the last "classic" version of the program. But, I see it can still be done via the web app.

  • Go to the 3D GeoGebra web app
  • In the input bar, type in some vectors. To type a vector, the notation is: Vector((starting point), (ending point))

enter image description here

  • You should see a typical 3D rendering of the vectors.

enter image description here

  • Now right-click somewhere on the graphing window, and you should see a pop-up window. Select the last option for Settings:

enter image description here

  • You should now get another pop-up/side-scroll window. Select the last tab for Projection, and click the button that looks like a pair of glasses.

enter image description here

  • Now the image should render as an anaglyph for red/cyan glasses.

enter image description here

  • This works with other functions as well. For example, $z = \frac{6xy}{e^{0.2x^2 + 0.2y^2}}$. [I don't have a pair of 3D glasses, so I cannot tell you how well this works in practice.

enter image description here

Edit

I forgot to mention the "animation" part of your question. You can rotate the image by clicking and dragging the image, but getting the image to automatically rotate around, say, the z-axis, requires a line or two of code and doesn't seem to run as smoothly as just clicking and dragging.

Nick C
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If you do want this effect (some of the comments are right that there may be other ways to achieve your pedagogical goal), Sage Math has a 3d viewer called "Jmol" which has this ability built in. Try this live example from the documentation, and right-click (Command-click on Mac) to get "Style", then "Stereographic", which will give you a number of options for this kind of viewing. Another example in the documentation which mentions this is a vector field plot.

Note that in the future you will need to use viewer="jmol" in any Sage 3d plot command as the default viewer is changing.

kcrisman
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