Updated March 7, 2012 I'm working with Erin Denenberg and Melina Nolas. We will be creating and explaining the constructions for parallel lines (using the angle copy method), a pentagon, and a 17-gon. We will then be taking the pentagon and turning it into a fractal. We will be delving deeper into any relationship (possibly a proportional relationship) between the pentagon with other pentagons and possibly other decagons.
Updated March 14, 2012 I never mentioned what the fractal actually looks like. So 10 pentagons put into the formation of a circular pattern is the first part to it. The outer point on the circular pattern were then connected, and this formed 10 isosceles triangles. The 10 triangles combined with the pentagons formed one big decagon.That is the first iteration of our fractal. We then made ten more pentagons and 10 more isosceles triangles using the sides of the decagon from the first iteration. This formed shapes that were bigger than the first set of shapes. This is the second iteration of our fractal. We then repeated these steps multiple times and got our fractal. The magic theory is a theory that states most regular polygons when rotated around corresponding sides create not only a circular pattern, but also the shape formed should have double the number of the sides of the original figure.
Updated March 21, 2012 Ok, we have now advanced a lot further in our project since my first post. We have now decided to get rid of our constructions part of the project and focus on fractals and our brand new magical theory.. Our first page is up and it contains our pentagon fractal. We did proportions between sides, and our ratio is 0.52 with the thousandths place ranging between 4-6, most of the places being the number 5. One of my partners is currently researching how to animate the fractal. If you have any idea how to animate images, please contact me on this website or email me at email@example.com. I am now working with septagons and octagons, along with the magical theory, and ratios too. So I am pretty busy. I am also working with heptagons right now. I put them into a circular pattern and it worked out a bit different than what I expected. The outsides of the heptagons forms a 28- gon, 4 times than what it is supossed to be. But the inside forms a 14-gon. I will look into this problem some more.
Updated March 25, 2012 So we are still having a bit of problems with the animation. We have an idea now but still are not sure. Please contact me immediately if you know anything about animation at firstname.lastname@example.org. I sort of solved the septagon problem, but I have to move on to other mathematics. I handed it over to my partner, Melina. Melina is looking into the history of the fractal and filling out that section of the page. Erin is working on two different animations for the page of our fractal.
Updated April 2, 2012 Ok so now I am working with equations and handling almost all the math aspects of the project. I figured out that the proportions were 1.9 and 0.52 using two different methods involving multiplying or dividing the data.I put them into the form of basic summation equations. I used the quanities for the first five iterations and then used a variable. I did that twice, so there are two sets of equations using each number listed above. Feel free to take a look at it on the mathematical section on the pentagonal fractal page. The only mathI am working with right now is the proportions between the different sides of the iterations. Ummmmm I am having some problems with my final equation as of right now, its an expotenial equation. If you can help please email me at email@example.com. Thanks! Also feel free to email about any additional idea involing math and our fractal.
Updated April 6, 2012 Yay! I just figured out the exponential equation for the proportions. It toke me a while despite it being so simple. It turns out GSP gave me numbers that were a few tenths off due to zigzagged lines in the image, but we fixed it. So thats good. My exponential equation is 1.9 to the power of the number of the correspoding iteration. We should be finished up in about one week which is when the project is due.
Updated April 9, 2012 I am putting the finishing touches on the mathematical section of the page right now. PLEASE LOOK AT IT! I would like some nice critism on it soon, so I can fix it before next week when this project is due. But please only look at the proportions part of the math section not the magic theory section at the beginning. I am only in charge of the proportions section. Please feel free to email me with your comments at firstname.lastname@example.org.Or just leave the comments on my userpage. It would really be appreciated. Thank you!
Updated April 10, 2012 So the due date for my project is nearing. I still need help with a few things. If you could take a look at our page that would be great. Please give me any constructive criticism about what could make the math section better. Also if you have any idea about the magic theory( explained on the page)and the math behing it, please contact me. If you know anything our fractal resembles that you know a bit about, please contact me. We are having problems connecting our image to the real world. If you have a solution to any of these problems please email ASAP at email@example.com. I will respond promptly or leave a comment on the page.
Updated April 16, 2012 The project is due at the end of this week, I am really excited. An equation for the magic theory has been created and it has led to some pretty interesting findings. The math section will now expand a lot within the next few days. I related our image to hyperbolic tilings, optical illusions, and soon a really cool picture of some cauliflower.
Updated April 18, 2012 Ok so we are finally done this project. Yay! I really loved this project and I encourage that you go look at all of our hard work. Just click the link or type in Pentagonal Fractal in the sidebar. I hope you enjoy our Pentagonal Fractal. :)
Updated June 12, 2012 Ok, so it turns out we are not done the project. Well I got a grade for it ( 100!), but my math teacher would like us to work on it over the summer too, which is actually really awsome. I missed math images a lot and from the sounds of our mentor, it sounds like things are going to be a lot more fun now ( by that I mean exploring the math more, more connections, and remaking images so they look cooler). Wish me luck.
Email: firstname.lastname@example.org Page Name: Pentagonal Fractal Partners: Melina and Erin
This is our fractal and page. Pentagonal Fractal