A 3D printed knot

Here are two photos of the 3D model of the parametric surface:
x(u,v)  = cos(u)*cos(v)+3cos(u)*(1.5+sin(u*5/3)/2)
y(u,v) = sin(u)*cos(v)+3sin(u)*(1.5+sin(u*5/3)/2)
z(u,v) = sin(v)+2cos(5u/3)

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3D model finished!

My first attempt at a 3D printed model was finished today.   Next time I’ll refine the grid so that the surface isn’t so faceted, but I’m happy with the result.  I can’t wait to create more.



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CalcPlot3D has four built-in explorations which each contain a pre- and post-test.  Our current goal is to develop more explorations and to import these explorations into WeBWorK.

The current explorations, which should be accessed with Firefox, Safari, or Internet Explorer (not Chrome) are:

  • Dot product (10-15 minutes) focuses on the relationship between the angle between two vectors, the length of the vectors, and the value of the dot product.
  • Cross product (15 minutes) guides students to explore the relationship between the angle between two vectors, the length of the vectors, and the cross product direction and length.
  • Velocity and acceleration (1 hour) demonstrates the relationship between the velocity, acceleration, and position vectors using a variety of examples.
  • Lagrange multipliers (1 hour) reinforces the Lagrange multiplier formula through a series of examples of contour plots of surfaces and constraint curves.

If you are an instructor interested in using an exploration in your class, please contact Paul Seeburger to access your student responses.

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Shortcuts and Navigation Tips

These are a few tips that I share with my students during our first computer lab in which they are using CalcPlot3D independently.
Copying images from CalcPlot3D into a word processor document:

  • Click on the graph then typing Ctrl-c (or command-C on a Mac) to copy and in the word processor type Ctrl-v (or command-V) to paste.  Alternatively, you can find the copy command under the CalcPlot-3D the File menu.
  • After clicking on the 3D graph, typing Ctrl-p will turn the background white (this is more aesthetically appeasing if you want to use the graphs in a document). Clicking b will remove the box around the graph.

Repositioning the graph:

  • You can zoom in and out of the graph using your mouse wheel, but to reposition the graph on the screen without changing the window size, use alt-(arrow keys) to move the graph up, down, right and left.
  • The home key on the keyboard will reset the 3D view in the standard position with the z-axis pointing upward.
  • You can change the axis ranges by clicking on the graph and typing a,  or selecting Format Axis under the “View Settings” menu, or clicking the button which looks like a table in the upper toolbar.
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3D Model Take 2

Since the printer head broke during my first attempt at printing a 3D model, I took the opportunity to adjust my graph to something more interesting.

I showed my previous attempt to a few colleagues and students.  One former student told me it would be very helpful for him to see this model in class when we were covering the topic of the path of steepest ascent.  Another professor suggested I tweak the surface to include multiple relative maxima that have different heights.  Here’s what I came up with.


f(x,y)= sin(x)sin(y)x

In 12 hours, I’ll go back to the printer to see the result.


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3D model

My first attempt at printing a 3D surface from a CalcPlot3D generated file ended prematurely due to a broken printer head. But this gives me the chance to make adjustments to the surface for an even more interesting example.


3D surface created with a broken printer head.  Eraser for scale.

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This spring we are rolling out the new CalcPlot3D blog. Check back for applet updates, classroom examples, discussions, and announcements.

Another goal this spring is to print out 3D models of surfaces generated in CalcPlot3D to use in classroom demonstrations like the one below:

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