Talk:Pythagorean Tree

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Contents

Checklist for writing pages

Completed by --Xtian1 10:14, 26 July 2013 (EDT)

Messages to the Future

  • If someone can actually show what the limit of the area of the entire tree is, then please do it.
  • If someone can explain more about perimeter and derive more math, then please do it.

References and Footnotes

  • Not applicable for this page.

Good writing

Context

  • The title image is interesting and the concept is pretty cool.

Quality of prose and page structuring

  • Section title or first few sentences explain what section is about.
  • Each section is relevant.

Integration of Images and Text

  • Images are referred to.

Connections to Other Mathematical Topics

  • Explained relationship to Pythagorean theorem. Besides that not many other connections.

Examples, Calculations, Applications, Proofs

  • Numerical examples provided.
  • Proofs and relationship to Pythagorean theorem established.

Mathematical Accuracy and Precision of Language

  • All math is free of error (to my knowledge).
  • Tone is casual while still maintaining some rigor (well I tried to make this as beginning high school level as I could).
  • No new terms really show up.

Layout

  • Text is in short paragraphs and images are distributed throughout.
  • No awkward chunks of white space.
  • Text wrapping doesn't cause problems.
  • Images are in the correct location of the page.
  • Viewed in different window sizes and saw no problems.

Older Comments

Hello John and Enri,

Hope you two are having a relaxing summer break. I have a few suggestions for the page:

Image and Image Description (at the very top)
  • I really like how you created your own image for the page. Most people just copy and paste from some website.
  • In the image description, mention how the fractal has a starting point (the starting square) and how it is constructed in a particular order.
  • In the image description at the very top, say “The space between the squares is a right triangle” rather than “The space between the squares in each iteration creates a right triangle”.
Basic Description
  • Nice job on creating the gif! If you have the time, try to crop the gif so that only the Pythagorean Tree is there (not the surrounding window. This just makes it look prettier. Since GSP sucks at making gifs, I suggest drawing a large rectangle in GSP that surrounds the entire Tree. You can use this rectangle to crop the images to create a smooth gif. If you need help, just let me know.
  • Mainly watch out for verboseness (examples below).
  • 2nd sentence: Write “The hypotenuse of the triangle is directly connected to the square” instead of “The hypotenuse of the triangle must always be the one that is directly connected to the square”.
  • 3rd sentence: Write “the legs of it” rather than the “legs of said triangle”.
  • 4th sentence: Write “so the area of each new square is less than the area of the old square” instead of “so the square are smaller than the big one”.
  • Remove the 7th sentence: “When the angles of the triangle are changed, one is made bigger, and the other is made smaller.”
  • Change the 8th to the last sentence from “so the sides change too” to “so changing the angle changes the side”.
A More Mathematical Explanation
Visual Suggestions
  • Whenever you write expressions and equations outside of the math environment, make sure to only italicize the variables; don’t italicize numbers. For instance, make sure the 2 superscript in s2 is not in the italics; in other words put the only around the s. This change applies to numerical constants as well (0.5s rather than 0.5s).
  • For the sines and cosines, write them in the math environment as \sin or \cos rather than just typing sin or cos.
  • Whenever you multiply a constant to sine or cosine, you don’t need the * between it. If you make the previous fix, then the sin and cos will look different enough from the normal math environment letters that the reader won’t be confused.
  • Fix the equation Proxy-Connection : keep-aliveCache...
  • Crop out the white spaces surrounding the bottom 3 images. I suggest you place the images as thumbnails to the right or left so the text will curve around it. Let me know if you need help.
  • This is just a personal thing of mine. I just don’t like how the * looks anywhere; I prefer parenthesis, brackets, or even the center dot far more. If both of you are fine with how it looks, then leave it.
Content Suggestions
  • At the start of the mathematical explanation, rewrite the proof of how the sum of the area of the smaller squares equals the area of the larger square. You start with the Pythagorean Theorem, then show proving it is related to it. Instead, try to start with deriving the sides of the squares first (express a and b in terms of θ and s), then showing how the sum of the areas is equal to the area of the larger square. THEN state how the Pythagorean Theorem is related to all this.
  • When you talk about finding the general equation of the area for any iterations and give examples about it, remember to put () around n + 1 since you’re multiplying s2 by that entire number (order of operations).
  • You should write your NOTE: (right under the second to last image) under the derivation of the general equation because it’s an assumption of the equation.
  • When you talked about the perimeter of the 45-45-90 case, I didn’t see any mentioning of the perimeter; I only saw discussion of the side length. While the side length is a necessary topic to discuss, it’s not enough to convincingly derive an equation of the perimeter for any number of iterations.
  • Try to derive the surface area for any iteration. It isn’t easy, so it might take a while. If you don’t want/can’t do it, let me know.

Finally, I see two main options for the history of the tree:

1. Expand on it and make it a new section (history of something is not part of a more mathematical explanation).

2. Remove it.

That’s it for now. Great job on the page so far, and good luck.

--Xintong Tian 11:50, 2 July 2013 (EDT)
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