Roulettes and Art – 2

Continuing with our discussion of ways to produce interesting designs with the Roulette Generator (RG) for Winplot, Here are some hints on making more detailed designs using more than one function. Hint #5: Adding more graphs to the first: You may add other graphs by selecting the roulette and/or velocity equations from the Inventory (CTRL+I)…

Roulettes and Art – 1

For the last few post we have been exploring roulettes using the roulette generator (RG) for either Winplot or Geometer’s Sketchpad. These files use the equations      The derivative is given by the equations Notice that the derivative is also a form of roulette. To generate various roulettes by changing the values of R…

Roulettes and Calculus

Roulettes – 5: Calculus Considerations. In the first post of this series Roulette Generators (RG) are explained. Here are the files for Winplot or Geometer’s Sketchpad. Use them to quickly see the graphs of these curves by adjusting one or two parameters. While writing this series of posts I was intrigued by the cusps that appear in some of the curves.…

Parametric Equations and Vectors

In BC calculus the only application parametric equations and vectors is motion in a plane. Polar equations concern area and the meaning of derivatives. See the review notes for more detail and an outline of the topics. (only 3 items here) Motion Problems: Same Thing Different Context (11-16-2012) Implicit Differentiation of Parametric Equations (5-17-2014) A…

Parametric, Vector, & Polar Equations

In BC calculus the only application parametric equations and vectors is motion in a plane. Polar equations concern area and the meaning of derivatives. See the review notes for more detail. (only 3 items here) Motion Problems: Same Thing Different Context (11-16-2012) Implicit Differentiation of Parametric Equations (5-17-2014) A Vector’s Derivative (1-14-2015) Roulettes  This is…

Before Calculus

These are post about topics that students usually study before studying calculus. Some go back to Algebra 1 or earlier. You may want to share these ideas with the teachers of the courses that come before your calculus course. AP Calculus Prerequisites From the 2019 CED Teaching How to Read Mathematics (4-12-2013) Some suggestions on reading…

Polar Equations

Ideally, as with parametric and vector functions, polar curves should be introduced and covered thoroughly in a pre-calculus course. Questions on the BC exams have been concerned with calculus ideas related to polar curves. Students have not been asked to know the names of the various curves (rose, curves, limaçons, etc.). The graphs are usually…