### Multivariable Calculus project using Vassar College's interactive topographic map sandbox

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

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:

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

- 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.