# Talk:Cardioid

### From Math Images

### Xingda's Comments

**Reword the very first description**

- Make sure it's totally clear where the light source must be positioned in order to generate a cardoid.

**Trace of a point?**

- Change to the path of a point?

**Derive the equations for a cardioid, otherwise I'll skim over them.**

**Generating a Cardioid Using Other Shapes section**

- You need a more consistent organization for this section. Some of the parts have equations and some don't, and I think you should be consistent. Also, if you don't want to derive these equation too, at least make a note so that someone else can in the future.

- Make sure that you can create the diagram based on your description of it. That way, you can be sure that you're not confusing anyone.

- Make the caustic part more clear. I think it's confusing that you talk about reflective and non-reflective surfaces. Readers will just assume these things. Also, in this part you say a point light source, but I can't figure a point light source generating a cardioid. Finally, what is a catacaustic?

- In the conchoid section, does the length have to be 2d? It might be interesting to explain what shape will result if a different length is used. Also, define the diameter of a cardioid.

- In the inverse section, put a mouse over for focus. Also, say that k is the inversion radius.

- Define cusp

**Microphone section**

- Define pick up pattern, polar pattern, sound pressure level, etc.

- Where is the front of a microphone?

**Mandelbrot set**

- This totally came out of the blue.. it needs more explanation and a bunch of terms defined.

**Caustics**

- Consider putting this section under the other caustics section

### Active Comments

**Re-order the description of each way of generating a cardioid**

It sounds like the order we decided on when we talked was: 1) a description of the way of generating the cardioid (these will probably have to be a bit longer than they currently are), 2) introduction of the fancy term (evolute, etc. - you probably won't need to make anything a mouse-over given this structure), 3) equations (if and where we want them). (Abram, 7/9)

- I reordered these. 7/13

**Derive equations for the cardioid**

Maybe derive the basic equations for the cardioid, if that interests you. The easiest way is probably to derive the parametric equations for x and y, and then use those equations to show that the polar and cartesian equations also work. (Abram, 7/9)

** Refer the reader to images**

There are lots of places where it seems like you want the reader to notice things about a picture, or where helps explain text, but you don't explicitly refer the reader to the image (I understand the anchoring of images may come later). (Abram, 7/9)

**The microphone section is a little confusing and could be expanded**

The microphone section overall could be a bit more clearly written (I trust you to find a way of doing this). One question I have in particular is what shape the microphone itself is, if the "cardioid" doesn't refer to the shape of the microphone itself. Overall, it may help to use a picture to describe in some detail what happens with the microphone. The section could end up being a good twice as long as a result, but it seems worth it. (Abram, 7/9)

- It's not much longer, but I do think it's more clear and I've got a new picture. 7/13

**The Mandelbrot section is a bit confusing**

I can come up with specific ideas if you want. (Abram, 7/9)

- Yeah, we'll have to talk about this. I spent this morning looking for more information but I can't really find anything. I don't really understand what's on the page right now anyway, I just took it from Wikipedia. Maybe we can go over this? 7/13

**Remove those awful math terms from the basic description and why it's interesting**

Both these sections have words like "evolute", "caustic", etc. They don't bother me, because I know enough math to know that hardly anybody bothers learning what these terms mean, but a non-mathematical reader may get intimidated because they think that they really ought to know these things. (Abram, 7/9)