# Talk:Pythagorean Tree

Hello John and Enri,

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

- Visual Suggestions

- Crop out the white spaces surrounding the bottom 3 images. And I suggest you to place the images as thumbnails to the right or left so the text will curve around it (let me know if you don’t know how to do this)
- 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...
- 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
*s*^{2}is not in the italics; in other words put the*only around the*s*. This change applies to numerical constants as well (0.5*s*rather than*0.5s*).* - In the second half of the more mathematical explanation, write
*s*^{2}(0) instead of*s*^{2}*2.

- Specific Sentence Suggestions

- Mainly watch out for verboseness.
- 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”.
- In the Basic Description, 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”.
- In the 3rd sentence of the Basic Description, write “the legs of it” rather than the “legs of said triangle”.
- In the 5th sentence of the Basic Description, 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 sentence “When the angles of the triangle are changed, one is made bigger, and the other is made smaller.”
- Change the 2nd to the last sentence in the Basic Description from “so the sides change too” to “so changing the angle changes the side”.
- I’ll make more specific sentence suggestions later.

- Content and Style suggestions

- 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.
- 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, remember to put () around
*n*+ 1 since you’re multiplying*s*^{2}by that entire number. - You should write your NOTE: (right under the second to last image) under the derivation of the general equation, since it’s an assumption of it.
- 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.
- Expand the History of the Tree (if you can). Start a new section with it, since it is no longer under mathematical explanation.

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

--Xintong Tian 17:13, 1 July 2013 (EDT)