In plane view: an exercise in visualization

We offer a problem in visualization which uses multivariable calculus concepts. The problem is essentially to describe (mathematically) what we can see on one mountain while sitting on an adjacent mountain. We present how our students, working in groups, attack the problem and the issues which surround the solution strategies produced. We have successfully used this problem for a number of years in our courses, devoting several class periods and about 2‐3 weeks outside of class to student development of a solution strategy. The problem serves to develop visualization skills, verbalization of mathematical concepts, and implementation of problem‐solving notions in mathematics including gradients, optimization, integration, surface area, and programming.