An Attempt to Analyze Texts

My blog was created to look at "Sacred Geometry." I first looked at the Platonic Solids and sought to spark interest in their symmetry and potential connection to the natural world. This was a loose connection to the natural through a look at a sacred tradition called Ayurveda.

Now, I would like to take a slightly different approach. I will examine the Golden Ratio and also look at its connection to the natural world, but we will see this is a little less "sacred" and more scientific, since we can see much evidence that the natural world "uses' this ratio to order itself (though I don't know about you, I certainly see the sacred in the natural). Hopefully you will see what I mean!

I will look at a collection of 6 texts and make an attempt to analyze their readability. This means I will analyze their complexity and accessibility by taking a basic look at certain quantitative and qualititative measures. My quantitative measures will be from the Flesch Reading Ease and the Flesch-Kincaid Grade Level measures, both which look at word a sentence length. My qualitative measures will include thoughts of text structure, writing style, language, and prior knowledge needed for understanding.

With the quantitative measures, I will take about a paragraph from each source and plug it into a website, StoryToolz, that measures readability and outputs a score according to various measures. With the Flesch Reading Ease measure, a lower number means a higher difficulty in readability. The Flesch-Kincaid Grade Level measure is more straight forward, giving an explicit grade level where this text would be comfortably readable.

Enjoy!

Calculating Phi

Yorgey, Brent. “Challenge #1” The Math Less Traveled. wordpress.com, 08 March 2006. Web. 25 July 2014 <http://mathlesstraveled.com/2006/03/08/challenge-1/>

This is not a word heavy text. It presents a problem asking the reader to find the solution to what is called an infinite fraction.

The three dots at the end means that the sequence goes on forever.

Text complexity/accessibility:

Flesch Reading Ease:  68.7/100 (plain English)
Flesch-Kincaid Grade Level: Grade 7.1

This text has a nice structure. The formatting is clear and pleasing to the eye. It uses visual aids and complex relationships are explicitly stated. The writing style utilizes a familiar voice and creates a readable narrative, with a lighthearted and creative approach. The language is not too complex, though some of the sentences are long. There is needed a "creative leap" to solve the problem, but the author explains explicitly that no more than basic algebra is needed once that leap is made.

Why did I choose this text?:

I like this text because it is something challenging yet doable to get you thinking, then provides a nice answer for the equation of the Golden Ratio, which will come up in all the other texts I will analyze.

Think about this...:

I am linking the solution, but I implore you to try and figure it out before taking a peek. It may be tough, but you'll like yourself better for trying! Challenge #1 Solution

Geometric and Fraction Expansions of the Golden Ratio

Kelchner, Adam. “Geometric and Continued Fraction Expansion of the Golden Ratio” Wolfram Demonstrations Project. WolframMathematica. Web. 25 Jul 2014 <http://demonstrations.wolfram.com/GeometricAndContinuedFractionExpansionOfTheGoldenRatio/>

This site only includes 2 sentences, so to call it a "text" is not quite right. It is a tool that one can use to explore the iteration of the equation looked at with the previous text while providing a look at what is happening geometrically at the same time.

Geometric and Continued Fraction Expansion of the Golden Ratio from the Wolfram Demonstrations Project by Adam Kelchner

Text Complexity/Accessibility:

Flesch Reading Ease:  55.8/100
Flesch-Kincaid Grade Level: Grade 9.5

I love the interactivity of this program. One speed bump will be that the user needs to download a program to be able to interact with the demonstration, and this might limit some younger students from being able to use it. Though, once through that, the visual is appealing. It allows the user to take a step-by-step look at what is happening geometrically as the infinite fraction is iterated. I would include this after using the challenge from above, so the student will already be familiar with the fraction, and will gain some insight into its connection with the sequence of rectangles, which I feel many students will have seen. If not, then it will be a great introduction!

Why did I choose this text?:

I chose this text because it is interactive and allows the user to explore the fraction and geometric iterations in tandem, to help further understanding of this thing called the "Golden Ratio."

Think about this...:

Does it make sense why this fraction and this geometric representation are the same? Hint: think about what length the "golden" length is in relation to the length that is 1 unit.

The Golden Ratio

Pierce, Rod. "Golden Ratio" Math Is Fun. Ed. Rod Pierce. 8 Feb 2014. Web. 25 Jul 2014 <http://www.mathsisfun.com/numbers/golden-ratio.html>

This is an in-depth look at the Golden Ratio. It is a different look than that taken so far with the equation, and provides many other ways to think about this ratio. It also has a interactive part, but also has much more! I see this sight as the last in this series exploring just what is this "Golden Ratio."

Text Complexity/Accessibility:

Flesch Reading Ease:  81.9/100
Flesch-Kincaid Grade Level: Grade 6.0

Math is fun is a great website providing very readable and interactive explanations of anything mathematical. The structure of this site is wonderful. Everything is broken down and portioned into short sentences with pictures. It uses concrete examples and avoids irrelevant details, providing many different ways to think about and produce this ratio. The necessity of a student needing prior knowledge is low, as the page starts with an introduction before moving to more. 

Why did I choose this text?:

I debated if I should include this as an introduction before the challenge from above, as this goes through it all then ends up with the thought about the same equation. But, my thought is, the equation is doable with a simple understanding of algebra (and a creative leap!) so I liked putting that first, building up some mystery, then rounding it up in the end by seeing the same thing, now with all of this added knowledge. I chose this website precisely for how rounded and thorough it's look is at the Golden Ratio.

Think about this...:

What else can you think about that just looks beautiful but you don't know why? Can you maybe see some of the Golden Ratio in there?

Nature by Numbers

Vila, Cristobal. “Nature by Numbers Movie” etereastudios.com, 2010. Web. 25 Jul 2014 <http://www.etereaestudios.com/docs_html/nbyn_htm/nbyn_mov_youtube.htm>

This "text" is not a text, but a video. It is a piece of art that provides intrigue and wonder as it animates, very beautifully, where we can see the Golden Ratio, along with some other mathematics, in the spiral of a shell, the seeds of a sunflower, and the wings of a dragonfly.

Text Complexity/Accessibility:

The fact that this is a video doesn't allow me to apply an exact quantitative measure according to the measures I have been using. Though, I would say that this is slightly lower readability than the Math Is Cool website and slightly higher than the 2 sentences contained in the Wolfram Math website. Though, I can certainly speak to the video's structure. It is just a beautiful video. Even if a student comes away without a clear idea of what the Golden Ratio exactly means within the context presented, I feel that interest will be built nonetheless, and I at least hope that it will convince one that this proportion relates to the nature that is observed and animated. The language (mathematical language) is similar to that already presented, making it relevant to a student's prior knowledge.

Why did I choose this text?:

I have touched on this already a bit. My main goal is to build interest and (at least slightly) convince a student that this ratio is seen in the natural world. I want to create a sense of "aaahhhh" like a sigh, and a pleasant interest. It is a sort of scaffolding into the next text, which talks more in depth about the reality of this ratio in nature
.
Think about this...:

While watching this video, just let it sink in without hoping to understand everything. The Golden Ratio is about beauty in the end!

The Golden Proportion in Nature

O’Connor, Aidrian. “Phi / The Golden Proportion in Nature” Nature’s Word. 2010. Web. 25 Jul 2014
<http://www.natures-word.com/sacred-geometry/phi-the-golden-proportion/phi-the-golden-proportion-in-nature>

This text deals with much of what was seen in the video above. As we learned from higher up in this post, I like the mystery first then the closer look later. This text does this very much the same in relation to the video, looking at the angles presented and giving more words to the visuals seen in the video. It goes through many examples of plants and animals exhibiting the Golden Ratio, ending with a brief look at the human body.

Text Complexity/Accessibility:

Flesch Reading Ease:  61.7/100 (plain English)

Flesch-Kincaid Grade Level: Grade 12.7

This is the most complex of the texts I have chosen. Though, I hope that it is quite accessible because of the scaffolding I have provided with the previous texts. The grade level is high but the reading ease is "plain English." I think this means that it has long sentences but short words. Indeed, this is the case. Students shouldn't have much problem with the words in this text. If my job has been done, having built interest, I can only foresee a positive association with this information. Some of the math he talks about is confusing even for me, but it seems to make sense. Structurally, the paragraphs are short and the pictures are pleasant and helpful.

Why did I choose this text?:

I chose this text to build upon the knowledge and beauty shown in the video. The point of all of these texts is to talk about the Golden Ratio and to relate it to nature, which is another view of what is possibly "sacred." It talks about what is not talked about in the video, and provides more examples. It provides (I think) clear proofs for the claims that this nature "uses" this ratio and, further, that it in fact provides nature with the most efficient way to organize itself.

Think about this...:

I wonder, since we are a part of nature, would it follow that the things we create and find beautiful also conform to the structure provided by the Golden Ratio?

The Human Body and the Golden Ratio

Meisner, Gary. “The Human Body and the Golden Ratio” Phi 1.618 The Golden Number. PhiPoint Solutions, LLC. 31 May 2012. Web. 25 Jul 2014 <http://www.goldennumber.net/human-body/>

This text provides the finishing touch to this discussion of the Golden Ratio and nature, and what better way to connect to the information by relating it to something we all know so intimately well - our own bodies. The text doesn't calculate anything, but uses some knowledge, built already (which the reader can figure out I think), to create some lines that are then used to analyze the human body according to the Golden Ratio. At the end I really liked how it took a look at the number 5 and its prevalence throughout the human body, and even within the formula we looked at before! This also ties the whole thing in nicely with my infographic from post #3 and the discussion about there only being 5 Platonic Solids and (typically) 5 elements of the Universe. Really cool!

Text Complexity/Accessibility:

Flesch Reading Ease:  69.1/100 (plain English)
Flesch-Kincaid Grade Level: Grade 9.6

This text is not very complex. The only problem is that it is talking about human proportions, but we're all different right? I think this would create problems for some people, but my take on it is that it is just talking about a typically proportioned body, which I can accept. We can't talk about all possibilities all the time! The language is simple English and the grouped meanings are fairly short. It was nice that the author chose to only talk of 5 points of divine proportion, to keep with his idea of the prevalence of the number 5. 

Why did I choose this text?:

This text is all about the Golden Ratio and the number 5, which is why I love it. I have not talked a lot about the number 5 in this post, but in my previous post and infograph it was kind of all about the fact that there were only 5 Platonic Solids and 5 elements of the Universe. It is also very accessible by being about our own bodies, so we can experiment and see if it is all true. I really really loved the fact that the author was able to see the number 5 within the equation I started this post with, and to tie it all in further with the talk of the Platonic Solids, I mean, come on! What are the odds!

Think about this...:

While reading through this text, can you think of any other places where we can see these proportions and/or the number 5?