Third Semester Calculus

#### Spirographs. TeX version or Postscript version. If you get the TeX version then you should also get Figure 1 in Postscript or CorelDraw format.

Project contributed by Neal Brand.

This project requires students to derive parametric equations for the curves created by spirographs. Students are then required to compute arc length and investigate a conjecture concerning the arc length.

Project teaches and provides practice in- Deriving parametric equations
- Trigonometry review
- Use of computers to graph parametric curves
- Arc length of parametrically defined curves

#### Ants on a Doughnut. TeX version or Postscript version. If you get the TeX version then you should also get the figures in either Postscript of CorelDraw format.

Project contributed by Neal Brand.

This project is an introduction to differential geometry. Students compute lengths of various curves along a torus with the help of a computer.

Project teaches and provides practice in- Visualizing in three dimensions
- Coordinate systems for a surface
- Parametric curves in three space
- Use of computers to approximate integrals
- Arc length of parametrically defined curves

#### Isolating Perry Metric in a Quality Cell. TeX version or Postscript version.

Project contributed by Neal Brand.

This project is an introduction to the calculus of variation. Students are to investigate the largest area that can be enclosed by a closed curve of fixed length.

Project teaches and provides practice in- Parametric curves in two dimensions
- Lagrange multipliers
- Integration by parts
- Arc length of parametrically defined curves
- Area using Green's Theorem (Students not required to know Green's Theorem before the project.)

Return to the UNT project home page.