Multivariable Calculus project using Vassar's interactive topographic map sandbox

Check out these videos of the "augmented reality sandboxes" at other schools:

• https://www.youtube.com/watch?v=CE1B7tdGCw0
• https://www.youtube.com/watch?v=wZpR1ynhOfg
• https://www.youtube.com/watch?v=lurZEwKgdFo

It turns out that Vassar College has its own "augmented reality sandbox"!

Located in the Warthin Museum of Geology & Natural Science in Ely Hall near Main Building, this sandbox was built by Rick Jones and Chris Gahn:

(I tried to make the Vassar College logo!)

Assignment for MATH 220 Multivariable Calculus

We have been using the (fourth edition of the) textbook by Zill and Wright and have been studying Partial Derivatives in Chapter 13. Recall:

• Section 13.1 on Level Curves
• Section 13.2 on limits from different direction
• Section 13.3 on Partial Derivatives
• Section 13.6 on Gradient and Directional Derivative
• Section 13.7 on Tangent Planes and Normal Lines
• Section 13.8 on Extrema

Please complete the following assignment, with each student individually turning in answers to the bolded questions:

1. Form a group of 2 or 3 with students you have not worked with before.
2. Schedule a time to visit the Museum during the alloted hours, and receive confirmation of your timeslot.
3. Once there, build your own landscape. Make sure you have some useful features like hilltops, valleys, saddles, and hills of different slopes.
4. Answer the following questions individually.
   1. Draw your landscape using contour lines.
   2. Find at least one relative maximum. Label this point or these points with an asterisk *.
   3. Find at least one relative minimum. Label this point or these points with a hashtag #.
   4. Choose some point that is not a critical point. Mark it on your map as A. Draw a contour line passing through this point.
   5. Indicate with a vector the direction of the gradient at point A.
   6. Repeat Question 4 for a new point B. Try to find a place where the steepness of the hill is different from that at point A.
   7. Repeat Question 5 for the new point B.
   8. Compare points A and B. At which point does the gradient vector have a larger magnitude? How can you tell?
5. Take a photo of your landscape. If you choose to post it to social media, please use the hashtag #VassarSandbox

Want more to explore?

Check out this old topographic map of Vassar Farms:

Alternatively, take a walk around Sunset Lake and the adjacent hills and see if you can walk along some contour lines.