True-False Quiz Questions 17 and 18: Circular and Parabolic Cylinders in 3D

YouTube - Video notes - Video sections playlist - Vectors and the Geometry of Space playlist

In this video I show that a formula has different meanings when plotted in 2D vs 3D, such as the equation of a circle in 2D which becomes a circular cylinder in 3D. This is because when the 2D formula is extended to 3D, the z-variable is assumed and extends to infinity. Thus the circle formula represents the circular cross-section of an infinitely long circular cylinder. This is the same case for a 2D parabola extended to a 3D parabolic cylinder.

Timestamps

• Question 17: Formula for a Circular cylinder in 3D: 0:00

• Question 18: Formula for a Parabolic Cylinder in 3D: 1:22

  • Paraboloid is bowl shaped: 3:27