Geometric interpretation of the Jacobian

Consider the parabolic transformation and . The Jacobian establishes a relationship between the area of the blue square (left) and the area of the red region (right). Instructions:
  • Drag the green point (on the left) to change the position of the blue square. Observe what happens to the red region.
  • Drag the slider , which determines the side of the blue square. See what happens to , for small values of .
  • Zoom in or out, if necessary.