# 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…

# Hypocycloids and Hypotrochoids

Roulettes – 4: Hypocycloids and Hypotrochoids In our last few posts we investigated rouletts, the curves that are formed by the locus of points attached to a circle as it rolls around the outside of a fixed circle. Depending on the ratio of the radii (and therefore the circumferences) of the circles these curves are the…

# Epitrochoids

Roulettes – 3: Epitrochoids In the first post of this series Roulette Generators 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. The parametric equations of these curves are below. R and S are parameters that are adjusted for each curve. Before looking at Epitrochoids, consider the…

# Epicycloids

Roulettes – 2: Epicycloids In the last post we saw how a cardioid can be generated by watching the locus of a point on as one circle rolls around another circle with the same radius. In the first post of this series Roulette Generators are explained. Here are the files for Winplot or Geometer’s Sketchpad. Use them to quickly see the graphs of…

# Rolling Circles

A few weeks ago I covered some trigonometry classes for another teacher. They were studying polar and parametric graphs and the common curves limaçon, rose curves, cardioids, etc. I got to thinking about these curves. the next few posts will discuss what I learned. To help me see what was happening I made a Winplot…