§2.5.2 - Using a Range of Flat Planes:
The Elevated Level Curve Set

by Robert Curtis, Bill Davis, and Lee Wayand.

Range of Flat Planes Cutting the Surface

Shown in the MathView interactive to the right is an animation demonstrating the process of cutting a set of level curves on the surface S.

The resultant intersection curves are shown in black.

Associated to a selection of these level curves are the height values of the particular level curve. While not too important when these curves are elevated such as they are in this picture, these number will play an important role when we drop these level curves down to 2D.

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

Note: This interactive does not yet work in the current beta version of MathView.

Help for MathView math entry keystrokes

Changing the Number of Level Curves Shown

The number of level curves shown in a 3D graphic depends on how much detail you want in the picture.

You may adjust the number of level curves shown in MathView via the setting numberoflevels.

You will want to practice with this setting as you will need to make these adjustments in solving problems using level curves.

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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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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