Chapter 7 Relevance (Geometry Honors)

Part I (Relevance):

Big Idea: What is a circle?

Area of my life: computer fans

In the past year or so, I have picked up the hobby of messing around with computers. In the art of PC building, one of the most crucial elements is cooling. The most cost effective means currently used for cooling a CPU is the use of a direct copper contact heatsink with a small fan (Richie, if you are reading this please don’t comment). Fans are used all over a computer to cool components like the CPU and GPU and also to improve airflow in cases. How does this relate to this unit? The image of a circle created by the spinning fan is in fact, a circle. The center of the fan is the same distance to the longest points of the fan blade. When the fan blades spin, the longest point on the blades create the image of the circle. Every point of the “circle” is the same distance from the center, making the image effectively a circle.

Part II (Visual):

Image result for bmw logo

The BMW logo is a perfect example of 4 90 degree sectors of a circle. I can assume that the sectors are 90 degrees because all 4 sectors are intended to be congruent and since there are 360 degrees and 360/4=90.

Part III (Box of Chocolates):

The concept of shape hierarchy in Flatland is similar to the definition of a circle. A circle is defined as a figure whose boundary consists of points equidistant from a fixed point (the center). It is a much more complex shape to calculate (assuming you are using a non-rounded version of pi) and has an indefinite number of sides compared to normal polygons. This correlates to the reason why circles are considered the elite class because of their infinite number of sides. Additionally, since calculating the area and circumference of a circle involves a never ending number, circles in Flatland are considered superior since their size can never actually be calculated.

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Geometry 6.10.3 Relevance

Part One: Relevance

Topic: Area and Sectors

Area of my Life: ZIP codes

My ZIP code, 97302, is a sector of Oregon. I’m comparing Oregon to a circle and ZIP codes as sectors. If you wanted, you could find the fraction of area that your ZIP code takes up of your state, find the area of your state, and multiply the area of your state by that fraction to get the area of your ZIP code. This is exactly how you would find the area of a sector.

Part Two: Visual

Topic: Arcs

Image result for arc building

This is an example of arcs in real life, an arch.

Part 3: Analogy

Topic: Circles and Triangles

Area of my Life: Books (Harry Potter specifically)

  • The wizard community is a portion of the world, like a triangle inscribed in a circle
  • Harry Potter has two other friends, so they could be the three points of a triangle
  • The sign of the Deathly Hollows is an inscribed circle:

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Chaper 8 Relevence

  1. In our Robotics competition, sometimes by solving one problem we created another problem, and had to find a different way to fix the first problem. This is like the process of eliminating extraneous solutions which, in solving one problem, create another.

2. Here is a square root (also known as a radical sign with an index of 2)

Image result for radical sign in real world

Here is a cube root (also known as a radical sign with an index of 3)

Image result for cube root tree

3. In a complex number, there is a real part, and an imaginary part that can be interacted with despite being imaginary. In the movie The Velveteen Rabbit, the main sometimes is in the real world and sometimes in in n imaginary world he can play in and interact with, just like how a complex number is partly real and partly imaginary.

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Chapter 7 Relevance

  1. Big Idea: Circumference: The circumference of a tire can be used to calculate the distance it will travel in one revolution. This could be useful in calculating mileage.
  2. This entire chapter reminded me of the movie Flatland because of the hierarchy of shapes in the movie, and how it relates to the complexity of the formulae that you need to solve for various values in them.
  3. Circles relate to the book series Harry Potter because Harry’s personality keeps on relating back to his past, and a circle always comes back to the place it started. Also, he comes back to Hogwarts every year, and his children went to Hogwarts years later.
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Chapter Relevance: 8

Part I: Relevance~

Big Idea: (Two variable) Substitution

Area of my Life: Shopping in other countries

I travel a lot, and sometimes to other countries even. When I need to exchange money, there’s multiple times when I need to exchange money. You need to find how much you have in American dollars and then substitute that in for how ever much that sum is in the other country.

 

Part II: Visual~

This picture represents two variable matrices. The people could be seen as the second equation and the train could be the first. When the people get on and off it could be seen as adding or subtracting the second equation from the first.

 

Part III: Our Box of Chocolates~

Movie: The Lord of the Rings

Big Idea: Two Variable Systems: Graphing

 

  1. In the movie The Lord of the Rings there are multiple stories but they all have something in common. This could be seen in TVS: Graphing because there are always going to be two lines, and usually they cross at some point (unless they’re parallel lines)
  2. In TVS: Graphing you are always going to get some sort of answer. The answer could be a negative number or positive. In The Lord of the Rings (while you’re watching it) you know the movie is going to end sometime, but the ending could go either way (negative ending or positive).   
  3. In The Lord of the Rings, Sauron and the orcs are the bad guys. In TVS: Graphing, inequalities are the bad guys. They both have things that are just there to make your life harder.

 

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Chapter 7 Relevance – Geometry

A section in this unit that relates to my life is chords. It relates to the guitar and ukulele not only because of the music term, but because the strings over the sound hole look like lines that have two points on the edge of the circle. On the guitar there are six strings that are each chords of the circle that is the sound whole, and on the uke there are four.

In the above picture, notice the semi-circle by the free throw line and the bigger 3 point throw line (I have little knowledge about basketball, so I’m just hoping that those are the right terms…). They are each semi-circles, which are sectors of circles that we just can’t see the entirety of. They are also arches that measure 180 degrees.

The circumference of a circle reminds me of a clock. Specifically, how much the end of the hands travel. For example, if a clock has a diameter of one foot, the end of the second hand travels around the circumference of the clock, which is 3.14 in this case. You could also compare this to arch lengths if you wanted to find how far it traveled in an amount of time besides an exact minute.

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CHAPTER 7 DISCUSSION

 

PART 1

Big idea: Slope

Area of my life: Hiking

The next time I go for a hike, I may want to know how steep some of the terrain is. Whether I’m going downhill or uphill, a short fall straight down, or climbing up a vertical ledge, I will want to know what I’m in for and once I know how to calculate slope I can easily figure this out.

PART 2 visual

Image result for lined paper

This is a piece of lined paper, as there are many on my desk, I noticed that patterns and lines obviously show well in a piece of lined paper.

PART 3

A book I once, the Familiars, read can be looked at a parallel and perpendicular lines. The group of animals go along on their adventure with no scary plot things happening, then at some sudden points they pass by a lot of danger and defeat them, then always move on to go back to their mellow adventure.

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Chapter 9 Relevance

Part I: Relevance

Big Idea: Simple harmonic motion

Area of Life: Slinkies

My brother keeps a grey slinky on his place at the breakfast counter, and it models simple harmonic motion. If I took the slinky off the counter and held onto the top alone (assuming that other forces of physics like gravity and air resistance didn’t apply), the slinky would demonstrate a simple harmonic motion. Depending on how wide and how heavy a slinky is, the maximum displacement, frequency, and period will be different for each slinky. For my brother’s, which is fairly large, the maximum displacement would probably be a high number, and the period would be big as well.

Part II: Visual

This demonstrates one possible application of an arcsine. To find the angle formed at the tip of the boat, you can use an arctangent function which applies the ratio of the height of the lighthouse (a presumably known value) to the ship’s distance from shore (another presumably known value). The arctangent function uses a tangent ratio to find the angle which produces said tangent.

Part III: Analogy

Solving a complex trigonometric function structured like a quadratic equation using the Pythagorean Identity is like writing a test in another language.

First, you have to identify the language in which the test is written — identifying the equation as one that can be solved with the Pythagorean identity. Then, you translate the question into English (mentally or by writing it out on paper) — replacing the sine/cosine/tangent values in the function with placeholders like “a” or “x,” making it more comprehensible to the solver. Afterward, you must apply the rules of a quadratic equation to solve it, either by using the quadratic formula or by factoring; i.e., sketching or thinking over what you want to say in English before writing it in the other language. Finally, once the equation is solved, you must replace your placeholder with the trigonometric function to get the correct answer — writing out the final product in the foreign language, which is less familiar, but ultimately correct. You may have to narrow down your answers somewhat after that last step, in order to make sure your numbers are precise and are the values the question asks for, which is comparable to editing the finished product and picking out typographical or grammatical errors that you missed when writing the first time.

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Chapter 8 Relevance (Algebra II Honors)

Part I (Relevance):

Big idea: Dividing Radicals

Part of my life: Medicine

Other than the field of computer science/engineering, I have a passion for medicine (as some may know, I aspire to be physician’s assistant). One of the formulas used frequently in the healthcare field is used to calculate the Body Surface Area. The BSA is useful for calculating dosage amounts for certain medications and also for determining total burn area on a burn patient. The formula for calculating BSA is identical to dividing any other radical.  The equationImage result for how to calculate bsais the square root of Height x Weight/the square root of 3600.

Part II (Visual):

Image result for freeing from the matrix

By multiplying the complex number by their complex conjugants (when dividing radicals) you are turning the denominator from imaginary numbers into real numbers. This is similar to taking the red pill and escaping from the Matrix into reality.

Part III (Box of Chocolates):

Neo’s character development in The Matrix is similar to dividing radicals:

  1. Neo is living is a non-existent augmented reality. Complex fractions are technically divided by numbers that don’t exist.
  2. Neo meets the crew of the Neb and takes the red pill which allows him to enter reality. The complex fraction/division is multiplied by the complex conjugate and turned into a workable number.
  3. Neo becomes a functional part of the crews and gets butt-kicking kung fu skills. The remainder of the fraction is simplified and is put into a set of complex numbers.

 

 

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Understanding Bigger Thomas

Richard Wright’s Native Son presents a protagonist who acts reprehensibly — killing and raping — a protagonist with whom most readers, on face, could not sympathize. One whom I, at first, could not sympathize with. Bigger Thomas is cruel, even those who have done him no wrong, and manipulative, especially to those weaker than him. But we continue reading because we want to understand, and as the narrative unfolds, we understand more and more. Bigger Thomas is not innocent, but his guilt is not just his own. Guilt falls on the structures of privilege and oppression that lead him to murder, as well, a fact which only select few in the novel seem to realize — Bigger among them.

It is hard to imagine a character less suited to the role of protagonist than Bigger. He is neither kind nor particularly sympathetic, and the novel does not ask the reader to sympathize — that is, it never asks us to condone or agree with his actions. Rather, particularly towards the end of the novel, the reader is asked to understand where both sides of the trial are coming from. We are asked to evaluate his sentence not as a question of justice, but as a question of power. We know he is guilty of the crime. We know he has murdered, and furthermore, that he is guilty of murder beyond what the jury knows. But his lawyer suggests, and the novel asks us to believe, that the jury does not find Bigger guilty because he is guilty. They find him guilty because he is guilty and black — and even then, the role of actual guilt in the decision may be suspect. Wright himself, speaking through Bigger’s lawyer, Max, thoroughly deconstructs the court’s decision before it even happens. “This man is different,” he insists, “even though his crime differs from similar crimes only in degree. The complex forces of society have isolated here for us a symbol, a test symbol. The prejudices of men have stained this symbol, like a germ stained for examination under the microscope. The unremitting hate of men has given us a psychological distance that will enable us to see this tiny social symbol in relation to our whole sick organism” (383). Max’s verbose speeches can be considered microcosms of what Wright strains to impart throughout the book: “that the mere act of understanding Bigger Thomas will be a thawing out of icebound impulses, a dragging of the sprawling forms of dread out of the night of fear into the light of reason, an unveiling of the unconscious ritual of death in which we, like sleep-walkers, have participated so dreamlike and thoughtlessly” (383). The mere act of understanding Bigger Thomas, Wright hopes, will allot white American audiences some degree of understanding of black Americans.

Unlike some other critical pieces of American literature, Native Son cannot be read without context. America in 1940 was wrought with discriminatory laws and institutionalized racism — not so unlike America in 2017 as we would like to believe, but enough unlike it that the privileged can deny those issues’ continued existence. Regardless, a book of this kind, if it existed, had never before come into the public eye. The narrative of Bigger Thomas sketches out a caricature of the “sadistic Negro” ( as popularized by racist whites, and then gives us a window into his mind. Wright argues that any moral deficiency, if it exists, cannot be blamed upon Bigger himself, but upon the systems of power which defined his self-worth and understanding of consequence. For Bigger Thomas, death by white hand was inevitable. In a society ruled by people who hated him, what reason does he have to obey their laws? The question of ethics, clearly, is not a question of law. Bigger’s sentence, despite Max’s pleas and well-justified arguments, proves this. The question of ethics is a question of privilege. For Bigger, what is right is what guarantees his survival. He cannot afford to think past this. He has never been given the resources to think past this. But this cannot be explained to the group of people who have created the conditions necessitating his aggressive survival instinct. White people would never have let Bigger live. The minute he walked into the courtroom, the jury had made up its mind. Max fooled himself to believe otherwise.

So Bigger’s choice becomes reasonable. He tells Max, “I ain’t worried none about them women I killed. For a little while I was free. I was doing something. It was wrong, but I was feeling all right. Maybe God’ll get me for it. If He do, all right. But I ain’t worried. I killed ’em ’cause I was scared and mad. But I been scared and mad all my life and after I killed that first woman, I wasn’t scared no more for a little while” (354). Escape, for him, is the only relief. Rejection of the system that oppresses him, by way of defying its laws, provides the only freedom he has ever known from it. Bigger rejects the idea that white people have the authority to punish him — he names justice as a duty of God, and God alone.

At the beginning of this essay, I declared that I did not sympathize with bigger. I now revise that statement: I sympathize but do not agree. It is difficult to read a passage like that on 363 without feeling something for him — wherein Bigger, suddenly comprehending the reality of his situation,  “sank to his knees and sobbed: ‘I don’t want to die . . . . I don’t want to die . . . .'” (363). In the last book, Wright does everything he can to make us feel for his protagonist, to make us understand. Native Son begs of its readers what had been (and to some extent, still is) denied black people in America; sympathy. There can be no progress without understanding. The stereotype of the black criminal no more: Bigger Thomas is human, and the reader is demanded to see him as such.

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