Level Surfaces and Quadratic Surfaces

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

Let , , and be nonzero constants. We plot level surfaces for quadratic functions in three variables, which give some well-known quadratic surfaces:

[more]

gives ellipsoids; when , this is a sphere centered at the origin of radius .

or give elliptical cylinders with symmetry axes along the axis and axis, corresponding to and .

gives elliptic paraboloids, opening up or down as or .

and , with , give elliptic cones. For , the level surfaces are hyperboloids of one sheet.

() and () give hyperboloids of two sheets.

[less]

Contributed by: Ana Moura Santos and João Pedro Pargana (Instituto Superior Técnico) (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send