# Polar curves

1. May 13, 2014

### influx

Why doesn't r = a(1+cosθ) have a dimple? I mean p=1, q=1 so q≤ p<2q and therefore r = a(1+cosθ) should have a dimple (like the curve in the bottom right corner of the image above)?

2. May 13, 2014

### LCKurtz

It does have a dimple with a point. If q gets any smaller it loops inside itself.

3. May 14, 2014

### influx

Is that considered to be a dimple? I thought dimples have a ''flat'' shape to them like the curve in the box on the bottom right?

Also, according to this page:

http://www.jstor.org/discover/10.2307/3026536?uid=3738032&uid=2&uid=4&sid=21104158779553

A cardioid doesn't have a dimple? (Table 1)

Thanks

4. May 14, 2014

### haruspex

Whether the cusp of a cardioid is regarded as a degenerate loop, a degenerate dimple, or distinct from both, doesn't strike me as terribly important. If I tell you a curve is an ellipse, does that mean it's not a circle?

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