Rose (mathematics)

Roses specified by the sinusoid $r = cos(kθ)$ for various rational numbered values of the angular frequency $k = .mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}⁠n/d⁠$ .
Roses specified by $r = sin(kθ)$ are rotations of these roses by one-quarter period of the sinusoid in a counter-clockwise direction about the pole (origin). For proper mathematical analysis, $k$ must be expressed in irreducible form.

In mathematics, a rose or rhodonea curve is a sinusoid specified by either the cosine or sine functions with no phase angle that is plotted in polar coordinates. Rose curves or "rhodonea" were named by the Italian mathematician who studied them, Guido Grandi, between the years 1723 and 1728.^[1]

^ O'Connor, John J.; Robertson, Edmund F., "Rhodonea", MacTutor History of Mathematics Archive, University of St Andrews

[1] O'Connor, John J.; Robertson, Edmund F., "Rhodonea", MacTutor History of Mathematics Archive, University of St Andrews

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