Talk:Involute of a Circle

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Chengying Wang 3:44 11 June, 2012

Hey, Wyatt! My name is Chengying and I'm a rising sophomore at Swarthmore College.

It's really interesting that I just recently started adding more material to the involute page left from 2009. What a coincidence that we have similar topics!

I think you did a fantastic job describing what an involute of a circle is, and I'm very impressed by your work in the more mathematical explanation part. Also, the why interesting section is really good. The involute gear is exactly the application I had in mind when I was planning my page. Great job that you realized this application!

The following are some of the comments I have that might help you improve this page more:

  • The three images you have are very informative. Nice choice. Just a reminder that it is a good idea to include the website url you got the image from or your name if you created it yourself in the comment section when you upload the images. There might be no way to change the comment of the image anymore, but just keep in mind for your future works.
  • In the basic description section, your sentence, "Every 360 degree rotation the ball makes the string shortens or lengthens however many inches thick that the pole is." is not very clear. I don't think "thick" is the appropriate word here and the readers might be confused. I suppose what you are thinking is for every rotation, the string lengthens or shortens by the circumference of the pole.
  • In the more mathematical explanation section, generating your own image using a computer software (e.g.geometer's sketchpad) is a much better way to illustrate the problem. In most cases, it is not a good idea to ask the readers to imagine the circle having a radius of 2 when it actually isn't. In addition, your letter markings of the angles and lengths would look much nicer and clearer if they are in print. Or, you can just use "AD" to denote the length of the base of your triangle. Then there will be no need to use "a", "d", "r" at all.
  • In the same section, it seems that at first you assumed the radius of you circle is 2 and then changed to the general case that radius equals a. While your result is correct, some of the facts you used, such as d = a θ', were not derived as a general argument. You only showed that it works for the case a = 2. Try to write a more general proof using a as an unknown constant.
  • A minor mistake: in your argument "So if r=\sqrt{2^2 + \pi^2} then \pi^2=\sqrt{r^2 + 2^2} and using variables...", you mistakenly used a plus sign in the second equation. Don't forget to correct it. :)
  • Something you can consider adding to the page: You successfully found the value of θ when the string is parallel to the x-axis for the first time as it unwinds. What about the second time? What if the string is not parallel to x-axis? I guess you haven't learned much about the coordinate system and parametric equations yet, but when you do, consider deriving an equation of the involute curve (pretty sure you saw those when you were looking at the wikipedia page). If you are interested, look at the involutes of other curves. Circle is not the only curve that has involutes.

I hope these comments make sense and are helpful to you. Feel free to ask me questions. You can find my contact information on my user page.

Overall, you did a great job on this topic. Keep it up!