## Explorations

(Revision October 2018: these explorations are no longer available in survey monkey and have now been imported into WeBWorK.  If you would like to use these explorations in WeBWorK, please contact vandieren@rmu.edu)

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.

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### 2 Responses to Explorations

1. Kitsos Tripos says:

Dear Paul,
Thank you for making available your excellent work.
I have entered x: a * cos(t+b) * sin((t+pi)/2)
y: a * sin(t+b) * sin((t+pi)/2
z: a * sin(t)
Where initially a =1 and b=o
I need to enter many such equations to create a solid. Any suggestions?
Could your program perform iterations in a loop?
It also seems that after several of these equations the program malfunctions, probably it runs out of memory. Please help!
Thank you again
Kitsos

Like

• Paul Seeburger says:

Hi, Kitsos!

I am not sure, but I believe you intend to generate a surface using the parametric space curve you stated, by varying the parameter b. Am I correct?

You cannot generate a surface using a space curve in CalcPlot3D, but we can use it to help us specify a parametric surface that does generate a surface by varying the parameter b in your parameterization.

Here we’d get the parametric surface with the following parametric equations in terms of parameters u and v:

x = a*cos(u+v)*sin((u+pi)/2)
y = a*sin(u+v)*sin((u+pi)/2)
z = a*sin(u)

with 0 <= u <= 2pi and -2 <= v <= 2.

The parameter a simply seems to change the size of the curve or surface, and not the shape or position.

You can actually use your curve in conjunction with the parametric surface to see how as you vary the parameter b in your curve, it will sweep out the parametric surface.

Here is a link that should open CalcPlot3D with this example in it: https://tinyurl.com/ya68qcwt