Spiral

A spiral is formed with a simple equation . The graph below set 'a' as positive, therefore there are two equations for you to tick. Choose whichever equation you prefer, you may choose both as well, then drag the value of 'a' according to your preference. Then, drag the value of to view the forming of spiral.

Betty, Created with GeoGebra

Rose

For the equation or , a rose is formed. The number of petal depends on the value of 'a'. Try to drag on the value of 'a' and compare the results when 'a' is even and when 'a' is odd.

Betty, Created with GeoGebra