Getting Ready

Today we continue to look at some previous posts that I hope will help you and your students throughout the year. We begin with some posts on graphing calculator use and then a few general things in three posts on beginning the year, followed by some mathematics I hope students know before they start studying…

Amortization

This is an example of how sequences and series are used in “real life.”  It could be used in a calculus class or an advanced math class. When you borrow money to buy a house or a car you are making a kind of loan called a mortgage. Paying off the loan is called amortizing…

Extremes without Calculus

There was an interesting question last week on the AP Calculus Community Bulletin Board. A teacher was working with polynomial functions in her pre-calculus class and the class had learned how to find the roots, and how the roots and their multiplicities affected the graph. Her question was whether there is a way to determine…

Limaçons

When I first started getting interested in roulettes I began in polar form graphing limaçons. Without going into as much detail as with the roulettes, I offer just one today. I found this Winplot illustration instructive as to how polar graphs are formed and just how the graphs work and relate to rectangular form graphs…

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…