References


Technology/Technology Tips
Technology Tips: Useful Online and Teacher Production Tools of The Geometer's Sketchpad

Jennifer Nickell
April 2007, Volume 100, Issue 8, Page 565
Abstract: 
This issue: Using Geometer's Sketchpad in the classroom. Technology Tips focus on how technology can aid teachers in using technology to enhance instruction, assessment, and the curriculum to help their students deepen conceptual knowledge.

Keywords:
Article
Grades 9-12
Teacher
Lesson Plans
Problem Solving / Problem Posing
Technology
Shapes


Spaghetti Sine Curves: Virtual Environments for Reasoning and Sense Making
S. Asli Özgün-Koca, Michael Todd Edwards, and Michael Meagher
October 2013, Volume 107, Issue 3, Page 180


Interactive environment with multiple applets
http://illuminations.nctm.org/lesson.aspx?id=2417



Direct result of technology in the classroom
<iframe width="560" height="315" src="//www.youtube.com/embed/uh_BEtsxk-U" frameborder="0" allowfullscreen></iframe>

Lesson Plan References
Fowler, D. H. "Ratio in Early Greek Mathematics." Bulletin of the American Mathematical Society 1.6 (1979): 807-47. Print. The “Ratio in Early Greek Mathematics” by D.H. Fowler, gives us the basic knowledge and history of ratios in early 200BC. The pdf is filled with references of Euclid’s Elements.  He defines the severally definitions of ratio and analyzes theories behind them.

Freitag, Mark. "Golden Ratio." Golden Ratio. N.p., n.d. Web. 03 May 2014. Mark Frietag tells readers about the golden ratio and how to properly use it. We get a clear understanding from where we can use this and what it applies to. 

"History of Phi, the Golden Ratio." Golden Ratio. PhiPoint Solutions, LLC., 13 May 2012. Web.  <http://www.goldennumber.net/golden-ratio-history/>. Created by an anonymous author, this author, as well as website, provides information on the who first discovered and used the golden ratio. The website also allows viewers to learn more on the basics of phi and the the applications of the golden ratio. The site gets more in depth about examples and allows contributors a chance to input their studies and research on phi.

"Golden Ratio." YouTube. YouTube, 25 Sept. 2008. Web. 03 May 2014. <https://www.youtube.com/watch?v=fmaVqkR0ZXg&list=HL1399165470>. Youtube user bricke321 gives us a view of several examples of where the golden ratio is found. Because this is a video, bricke321 gives a great example of the golden ratio that can only be received through sound.

Katz, Victor J. A History of Mathematics: An Introduction 2nd ed. Boston: Addison-Wesley, 2009. Print. This textbook, by Victor Katz, provides a solid background in the history of mathematics, helping readers gain a deeper understanding of mathematical concepts in their historical context. This book’s global perspective covers how contributions from Chinese, Indian, and Islamic mathematicians shaped our modern understanding of mathematics. This book also includes discussions of important historical textbooks and primary sources to help readers further understand the development of modern mathematics. Pertaining to ratios, the text contains a short portion of the study of ratio done in medieval Europe. 

Math Is Fun. "Golden Ratio." Golden Ratio. N.p., n.d. Web. 01 May 2014. <http://www.mathsisfun.com/numbers/golden-ratio.html>. This site is by an anonymous author. However, the website is very helpful with giving understanding the rectangle form of the golden ratio. It also gives an explanation of the helix function and where you can find the golden ratio.


Joyce, David. “Euclid's Elements, Introduction.” Clark University, 1998. Web. 6 May 2014. <http://aleph0.clarku.edu/~djoyce/java/elements/>. Euclid & the golden ratio, music, “extreme and mean ratio,” Greeks & golden rectangle, name for phi came from a sculptor, Phidias who made the Parthenon statue that embodies the golden ratio.

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