# Rose

### From JSXGraph Wiki

A **rose** or **rhodonea curve** is a sinusoid plotted in polar coordinates. Up to similarity, these curves can all be expressed by a polar equation of the form

If k is an integer, the curve will be rose shaped with

- 2k petals if k is even, and
- k petals if k is odd.

When k is even, the entire graph of the rose will be traced out exactly once when the value of θ changes from 0 to 2π. When k is odd, this will happen on the interval between 0 and π. (More generally, this will happen on any interval of length 2π for *k* even, and π for *k* odd.)

The **quadrifolium** is a type of rose curve with n=2. It has polar equation:

with corresponding algebraic equation

### The JavaScript code to produce this picture

var b2 = JXG.JSXGraph.initBoard('box2', {axis:true,boundingbox: [-10, 10, 10, -10]});

var f = b2.create('slider', [[1,8],[6,8],[0,4,8]]);

var len = b2.create('slider', [[1,7],[6,7],[0,2,8]],{snapWidth:1,name:'len'});

var k = b2.create('slider', [[1,6],[6,6],[0,2,12]],{snapWidth:0.2,name:'k'});

var c = b2.create('curve', [function(phi){return f.Value()*Math.cos(k.Value()*phi); }, [0, 0],0, function(){return len.Value()*Math.PI;}],

{curveType:'polar', strokewidth:2});