A note on Laguerre-type and Euler-type Grandi’s roses

Starting from the connection between the cartesian and the polar equation of a given curve, we introduce two different types of Grandi's roses (also called rhodoneas curves) with integer degree. The first extension is connected with the Laguerre-type exponentials, and the second one deals with the Euler's nearly cosine series. Several graphs of the relevant curves are shown, derived by the first author using the Mathematica computer algebra program. AMS 2010 Mathematics Subject Classifications: 33C99; 12E10; 42C10; 42C05.