Extending Surface Equations Integrated Math 4 Mrs. Tyrpak.

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Presentation transcript:

Extending Surface Equations Integrated Math 4 Mrs. Tyrpak

Nonlinear Surface Equations

What equation would an ellipsoid have in 3-space with the following measurements: 1.Axis along x-axis = 8 2.Axis along y-axis = 6 3.Axis along z-axis = 4

Symmetry in 3-space Recall symmetry in 2-space: Is this ellipse symmetric with respect to the x-axis? The y-axis?

Symmetry in 3-space Is the ellipsoid symmetric with respect to the xz-plane? the yz-plane? xy- plane?

Matching

Surfaces for Matching 1.Double Cone 2.Hyperboloid of 1 sheet 3.Paraboloid 4.Elliptical Paraboloid

Intercepts: Traces: Symmetry:

Intercepts: Traces: Symmetry:

Intercepts: Traces: Symmetry:

Intercepts: Traces: Symmetry:

Two Ways Plane Curves can generate surfaces: 1.A line (perpendicular to a plane in which the curve is drawn), to trace the curve generating a cylindrical surface 2.Rotate a curve about a line to get a surface of revolution

Examples: Cylindrical Surfaces: Surface of Revolution:

You know what I’m going to say! Awesome job!! Don’t forget to complete your extension and enrichment worksheets before you move on. Remember you are a mathematician