MATH 423, Exam 2

Due by Monday April 11

1. Normal sections

The animation below shows a surface $S$ as the graph of $z = x^2 - y^2$ plotted in the $xyz$ Cartesian coordinates. Normal sections of $S$ at the origin at varying orientations are plotted as yellow curves. Calculate and plot the curvature of the yellow curves at the origin as a function of the section's orientation.

2. Making a Möbius strip

Here are two animations that show Möbius strips being formed. Make an animation resembling one or the other, or improve on these with a cooler idea.

3. The fundamental forms of the Möbius strip

Calculate the coefficients $E$, $F$, $G$ and $e$, $f$, $g$ of your Möbius strip's first and second fundamental forms.