§2.5.3 - Dropping the Level Curves to 2D

by Robert Curtis, Bill Davis, and Lee Wayand.

Dropping the Curves

Shown in the MathView interactive to the right is an animation demonstrating the process of dropping a set of level curves on the surface S to the x-y plane.

This is where level curves are usually presented and used for analysis of the surface S.

Notice the numbers that MathView places on some of the level curves: it is their height on the surface.

This information is not very useful when the level curves are elevated onto S, but the information is very useful (and necessary!) when the level curves have been dropped onto the x-y plane.

The goal of this interactive is to strengthen your visualization skills is recognizing the resultant shapes of the level curves in 2D, and the picture of the parent surface's shape.

These skills will useful when we modify the process

3D Surface --> 2D Level Curves
to the reverse:
2D Level Curves --> 3D Surface

Try experimenting with other surfaces:

  • z = x2 + y2
  • z = x2 - y2
  • z = x2 - x y - y + sin(2x)
  • z = x3 - x y2

Help for MathView math entry keystrokes

Road Map
  • VR & 3D Calculus Home Page
    • §2.4 -
    • §2.5 - Level Curves
      • §2.5.1 - A Single Level Curve
      • §2.5.2 - Elevated Level Curve Set
      • §2.5.3 - Dropping Level Curves to 2D
      • §2.5.4, §2.5.5, §2.5.6, §2.5.7, §2.5.8, §2.5.9
      • §2.5 Exercises
    • §2.6 -

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Official Website of
www.calculus.net
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Core Development Team
  • Robert R. Curtis
  • Phil R. Smith
  • Christopher A. Barker
  • Diane Welden Housken
  • Tim Lance
  • Bob Stein
  • Donald Hartig
  • Lee Wayand
  • Charlene Beckmann
  • Bill Davis
  • Paul Latiolais
  • Dennis Sentilles
  • Carmen Artino
  • Michael Colvin


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