Talk:Polar Equations

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Final round of comments

  • Can you clarify the following two sentences:
  • "The spiral can be used to square a circle and trisect an angle"--Maybe add another image showing what you mean?
  • "This spiral's pattern can be seen in disc phyllotaxis." --Define disc phyllotaxis

I added a quick explanation on squaring a circle and trisecting an angle, as well as links to more thorough explanations under related links. In the future work section, I also made a note that pages can be created to focus on those topics. I also defined disc phyllotaxis. Thanks for reviewing!

Wow, Jen, this page is amazing! You've added a lot to it :)- 11:38 25 July 2011 Nordhr

I was thinking that for your app you could have a button to pick colors instead of having one pre-chosen. - Nordhr (6-24-11)

I'm not really sure what that strange div tag is from. I added an open div tag to make it go away, but I'm not sure how to really fix it. - Nordhr (6-27-11)

Nice pictures, love the spirals, good color combos, very intriguing. :)

Nordhr 14:38 6 July 2011

Tyler Sammann (sammat)

17:54 1 July 2011
After I drew a graph with the applet, I scrolled until the applet wasn't visible anymore, and when I scrolled back down the graph had been erased :(

Jenn Chan (chanj)

I think it's a Java Applet thing. It does that... :(

Response to Checklist

You'll find my comments in red 7/10 AnnaP

Messages to the Future
I have included a section discussing possible future works.
References and Footnotes
I have posted links and referenced the textbook I used to write the page.
I have included a brief section on how the topic is applied to real life.

  • It'd be really nice if this section could be expanded a bit. It's also okay to say that part of why this topic is interesting is just that you can use this method to create pretty images I have expanded that section and also included two images.

Quality of Prose and Page Structuring
I tried making everything as clear as possible by putting things in bullets.

  • Though this does work, it means that some of your explanations are a bit too brief. For example, in your bulleted list of ways to get different numbers of petals, it'd be great to have at least one small example image (along with the equation used to create it). I added pictures and examples (which is hidden under examples) for the bulleted list under "rose," and I added another image under limacon and numbers, so I can reference them.
  • It'd be really helpful if you added some text to go along with each of the other types of polar curves to explain a bit about each curve. Just one or two sentences per type of curve/spiral could be enough. Interesting facts or descriptions were added under the curve images.
  • I suggest not including this sentence: "Note that the difference between sine and cosine is  \sin(\theta) = \cos(\theta-\frac{\pi}{2}) . " until the more mathematical explanation so that you don't scare off readers with an equation so early on. I moved that to the "Rose" section.

Integrating of Images and Text
I have a lot of big colorful images of different polar graphs along with their equations.

  • It would be really useful to include an image to explain your equation for the area of a sector of a circle--just to show a circle, with the area of a sector shaded in and the angle theta labeled. I added two images in that section for the area of a circle and a polar curve.

Connections to other mathematical topics
A page on cardioid is already made, so I linked to that.

  • Why don't you link the helper page Polar Coordinates very early on in the page? That would help some readers. A link is posted under "Basic Description."

Examples, Calculations, Applications, Proofs
I have included an applet to graph polar roses, so it proofs the bullet points I made on the coefficient of the angles above.
Mathematical Accuracy and precision of language
I used latex for my equations, and I have included formulas to find the derivative, area under the curve, and arc length.

  • In your section on the derivative, you should mention that you don't have to take the derivative in cartesian coordinates; you can find  \frac{dr}{d\theta} and talk a bit about what the derivative represents in that sense (Let me know if you need help with this!) I mentioned that turning them into parametric equations is necessary, and gave a short definition of a derivative (I don't think there's a page explaining derivatives and slopes, wish I could link to it). I also added an example hidden under show more.

As you can see, I have divided things into sections with headers, so the information is easy to find.