Previous Koch Snowflake Discussion
From Math Images
1. Are the words that you define bold? YES 2. Do you have references and other interesting links? YES 3. Did you cite your pictures, or say if you created them? YES 4. Have you considered all of the comments on the discussion page? YES 5. Have you looked over everyone else’s pages, and linked to the relevant ones? YES
I've created an applet for the Koch Snowflake if you want to use it on the page, let me know if you have any comments or suggestions: Koch Snowflake
- Great! It can take the place of the first animation in the Basic Description.
- Ryang1 (7/6)
I really like this page the use of the images is very well planned. I do have a couple of things that are bothering me though.
- Since one of the big points of this shape is that the perimeter is infinite, when you show the formula for the perimeter it would be nice to see the infinite case.
- In the area section, I got a bit lost, I think if you showed the A_0, A_1, and A_2 cases and how they build to the rest of what you have it would be much clearer.
- Also, if there were a diagram or the labels were all at the beginning of lines or something, just to emphasis what the various labels are, or to emphasis their definitions, would be helpful.
- Thanks for your comments David! I made various revisions to this page based on your suggestions.
One more thing that I would change here is giving examples when you're calculating the perimeter and area. Start by saying something like "before iterating, the perimeter is __" then "after the first iteration, it is ___ =____" so that you build up the expression for the reader.
--AnnaP 22:26, 18 June 2009 (EDT)
- Sure, I'll see what I can do, but I'm just afraid that this may make the explanations too clutter.
- Ryang1 (6/29)
I can see why this page has been listed as ready for the public. Ideas are expressed clearly and correctly, and the page is well-polished too. Well done!
I do have one suggestion, though, that I feel kind of strongly about.
- With a ever-increasing number of sides, the perimeter of the Koch snowflake will infinitely lengthen.
This statement suggests that the perimeter going to infinity is a necessary consequence of the number of sides going to infinity, but it isn't that simple (the area is also constantly increasing, but it converges). You have a nice derivation of the infinite length below, but I think it's a good idea to write the sentence in such a way as not to implicitly suggest that because one sequence (the number of sides) diverges, any related monotonically increasing sequence (the perimeters) necessarily diverges. After all, the fact that the perimeter increases monotonically and diverges, while the area increases monotonically but converges, is part of what makes this shape so interesting.
- Thanks Abram! You bring up a great point.
- Ryang1 (6/29)
The last paragraph of the basic description is a little bit confusing. It looks to me like the area of the snowflake is bigger than that of the triangle, so saying that the snowflake's area is "5/8 of the original triangle" is not quite right, or at least unclear. Can you try rewording that? (for me, this would imply as opposed to the you state later).
I'm also not convinced that the snowflake is an example of an iterated function, per se. I think it's more of an iterated process, which is a bit different. I also think that mentioning that it comes from an iterated process and talking about infinite self similarity should be separate paragraphs.
- Thanks for catching my mistake- you're right I made an error when reporting the area in the Basic Description. I also made changes to refer to the snowflake as an iterated process as opposed to an iterated function.