From the first time that we used such inter-active geometry programs as The Geometer's Sketchpad and Cabri Geometry, we were intrigued by their potential to help students develop ways of thinking that underlie calculus and analysis (Cuoco, Goldenberg, and Mark 1995; Cuoco and Goldenberg 1997). One theme in this approach has been to look at optimization problems as geometrically defined functions, for example, the sum of the distances from a point to three fixed points. In an interactive geometry world such as Sketchpad or Cabri, the user does not need to impose coordinates on the plane and specify the distances algebraically at the outset. He or she may define the function directly as a geometric relationship; manipulate its variable (the movable point); and observe, numerically or geometrically, the value (sum of distances) that results. The algebraic step is also valuable; both geometric and algebraic interpretations lead to important insights. But the geometric step is often a particularly productive starting place for generating the ideas that one may want to revisit algebraically.