Area of Parametrized Surfaces and Wormholes
for Professor Sormani's Inspiring Talks series
Dr. Jorge Basilio (gbasilio@ucla.edu)
Updated: May 1, 2020
Playlist
Lecture Notes
Video Lectures
Surfaces of Revolution
Click the “Activate” button below to run an application that investigages wormholes as surfaces of revolution.Example: Wormhole 1
We investigate the surface of revolution determined by the curve: \( C: \begin{cases} x = t \\ y = \cosh(t) \end{cases} \) for \( t \in (-1,1) \)Example: Wormhole 2
We investigate the surface of revolution determined by the curve: \( C: \begin{cases} x = t \\ y = (1/2)t^2 + 1 \end{cases} \) for \( t \in (-1,1) \)Example: Wormhole 3
We investigate the surface of revolution determined by the curve: \( C: \begin{cases} x = t \\ y = 2+\cos(t) \end{cases} \) for \( t \in (0,2\pi) \)Arclength
Click the “Evaluate Sage Code” button below to run an application that numerical approximation to arclength.
Notice that computing the arclength of \(f(t)=2+\cos(t)\) leads to a difficult integral that SAGE can't compute a closed form answer. This is a so-called elliptic integral and there is no "elementary function" that gives us this value.
We need to compute the integral numerically as above.
If you want to see SAGE struggle and try to give the exact answer, run the code below (warning: might take a loooong time to evaluate).