The Evolute of the Cardioid
Let's look at the evolute of the cardioid. Use maple to plot it and find its equation. You can use
ParamPlot(evolute3(x,y), t=0..2*Pi, scaling = constrained); evolute(x,y); to create a paramplot if you have defined x and y. This will plot the function and return its evolute.
What happens when you take the evolute of the cardioid? Can you find a linear transformation (matrix) that models the evolute for this curve? (Hint: You will need to change the starting and ending values for t in order for your transformation to give the same function that maple gave. As long as t covers at least 2*Pi the function will sweep out the entire curve.)
[Back] [Part 2]