Circulation in 2-Space

This GeoGebra example dynamically illustrates the concept of circulation of a vector field along a closed path in two-dimensional space. It demonstrates how line integrals measure the tendency of a field to rotate around a curve. Core mathematical concepts include vector fields, line integrals, circulation, and the relationship between derivatives and integrals. The construction uses commands such as Sequence to generate points along the path, Derivative to compute tangent vectors, Integral to evaluate the circulation integral, Circle to define the closed loop, and Textfield for user input. Key objects include vector field components X and Y, their derivatives X' and Y', the circulation value I, and vectors v. This is suitable for university-level multivariable calculus courses, particularly when teaching Green's theorem and circulation, and can also serve as an intuitive tool for advanced high school students. Interactive inputs allow learners to explore how circulation changes with different paths or field configurations.