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Autumn Palen's Digital Portfolio

Stories with differering arcs

1. Rising Action

A visitor’s hand fell heavy on the front door. Over and over, a banging rang through the house. Any dog would be sufficiently loud upon coming across the sound of rustling leaves or a soft exhale. Knocking sent my dogs into a panic greater than any rational animal would have about anything ever. They each yelped urgently, thrashing their heads about and stomping their adorable little feet across the carpet. Despite deafness being a clear and present danger, I ignored the knocking, as well as the barking. After a short while, both had stopped, yet every five minutes, the knocking started up again, as did the barking. Thumping, pounding; repetitively, irritatingly. Finally, I could take no more. I tore the door open and shot a mean glare at the young man before me, ready to fight to the death. My arm swung back, my hand clenched together, and then, at the last possible moment, he spoke.

“Please don’t hurt me!”

“Why the hell not?” I wondered.

“I’m sorry I knocked again after you clearly did not want to answer the door, or could have very possibly not been at home.”

“That’s not good enough.” My arm was still raised.

“Please! It’s not my fault. I was born without the genetic ability to take a hint.”

I dropped my arm. “You’re free to go.” I whispered.

He was never seen or heard from again.

2. Noodle power
    Occasionally, I am faced with the annoyances that are solicitors. One in particular rapped on the door, paused, and rapped on the door again, as if the resident had magically appeared inside the house between knocks, or they just removed a pair of earmuffs, or perhaps their hatred of door-to-door salesman vanished mysteriously. I was not, nor have I ever been, one of those people. An additional burden to this ding-dong stayer is the fact that I have two tiny, floppy little dogs who go berserk when noises are made outside the front door. If someone breaks the sound barrier in China, those two dogs would be the first to know. If an explorer in the arctic has the sniffles, they are all over it. So, when some guy pounded on the aforementioned front door, it took every power in them not to explode. The cacophony of desperation was not kind to my ears, nor to my temper. I’d like to say that I tore open the front door and fought to the death with the man or woman who did not know how to take a hint, but I would be lying. I stayed seated, dead silent as if to imply to them that I am not home, and waited it out until someone hooked them away Vaudeville-style (I assume that is what happened).

January 31 2013

January 23 2013

two topics IN CALCULUS

Deriving a function, such as x^2 + 4x + 5, would result in having a function, such as 2x + 4, which is a tangent off of the original function. It is also a nifty (albeit convoluted) way to find the slopes of functions.

Piecewise Functions
Piecewise functions only conditionally fall under any given guideline set by a formula, depending on points along the x-axis. Said guidelines could be definite at each endpoint (two set points on either side), definite at one endpoint (one set point and one open circle), or not definite at either endpoint (two open circles on either side). Finding limits in this situation (a topic I did not discuss), is undefined when it is approaching a value from both directions which holds an open circle, even if there is a set point as well. There are ways around the lack of definition, such as approaching from the negative OR the positive side, or saying what the point is when x is at that point (the second option is only applicable if there is a set point).

January 18 2013


IN HIS OWN WRITE by John Lennon
1964, 80 pages

Read More

January 6 2013

The Problem of the Fortnight three

Problem Statement

This is an image of Pascal’s Triangle. The task for this fortnight was to find all of the missing numbers in the triangle (which involves finding an initial pattern), and then working backwards to discover any patterns that may spring to one’s attention once the triangle is completed.

Process Description

The pattern I noticed in order to continue filling in the triangle was one of addition. The lowest middle number in the incomplete triangle, 10, is the sum of 6 and 4, the numbers in the upper left and right corners. Further proving my point, 6 is the sum of 3 and 3, 4 is the sum of 3 and 1, and so on. The shell of 1s made around the outside of the triangle is due to there not being a second number in the left or right (or in one case, both) corner.


5 patterns within the complete image and describe why you found them interesting. You should strive to find unique ones to receive full points!

1. If the shell of 1s can be called the “first triangle”, then the “second triangle” goes up by 1 as it descends diagonally. This seems quite obvious, yet enchanting nonetheless, don’t you think?

2. Another sort-of obvious one: The triangle is mirrored. I’m easily fascinated, okay?

3. The sum of each line of the triangle is the sum of the previous line multiplied by 2. Funny how it turns out that way.

4. All of 11’s numbers (going diagonally from the “second triangle”) are divisible by 11. The same is true for 13’s diagonal line. And 15’s, technically.

5. The even numbers on that “second triangle” have less numbers divisible by themselves along their diagonal line than the odd numbers do. In fact, the amount of numbers that the odd numbers are divisible by increases as the even numbers’ amount decreases.

Self-Assessment and Reflection

This was a relatively simple problem, which does stand to make for a challenging write-up in terms of elaboration, seeing as there is not much to say that cannot already be instantly understood. I believe that I deserve a 10/10, because I finished the triangle and answered each question as thoroughly as one might think possible.

December 19 2012

Mindset: Chapter 5

I was stunned at how pigheaded some people of amazing statures can be. The example in this passage was Iacocca. He believed so fervently and relentlessly in his superiority that, once fired from the Ford corporation, he refused the wise outside opinion of his then-wife, who said, “You don’t realize what a favor Henry Ford did for you. Getting fired from Ford brought you to greatness. You’re richer, more famous and more influential because of Henry Ford. Thank him.” Every door closing is another window opening (figuratively), but Iacocca couldn’t seem to fit that concept through his fixed head.

    Jack Welch seemed like an impressively impressive man. The way GE’s worth skyrocketed under is rule is truly admirable. Nurturing tier after tier of employees must have been the main contributor to success. Visiting factories as often as he supposedly did must have given the workers a way to humanize the man who sat at the top of the pyramid they slaved under 40+ hours a week. Nearly everybody in the known universe hates their boss to some extent, and when it is amplified to the level of CEO? Pssh, menial laborers could easily despise him, even if he was the nicest man to have ever lived. Being near the people showed them that all in all, he was a human, just like they all were.
    Honestly, while growth mindset is totally pummeling fixed mindset, there are always a few innate elements from birth, whether environmentally or genetically, that impact the feeble, clay-like mind of a child. As someone who has watched at least four sports movies, I can tell you firsthand that people have the potential to overcome anything despite their economic standing or family history, but not every offspring of a given couple has the same hopes, dreams, and talents.
I am not at all a show-boaty, head-of-the-pack sort of person. I am a fly on the wall, and while, idiomly speaking, you can attract me with honey more than you can with vinegar, never once have I felt threatened by talent or intellect in another person. In this workplace, I’m not prone to affect anything at all, especially not good workers.

November 27 2012

Estimated Time of Derival

Critique Reflection
What problems did you ask for critique on?
4 o’clock, which is [d^5/dx 5x^5]/150
5 o’clock, which is 5.773502697(sin 60°)
9 o’clock, which is [d/dx (9x + 3)(2)]/2
and 10 o’clock, which is [(d^3/dx 4x^3 + 3x^2 + x) - 4]/2

What suggestions or comments pushed your thinking?
Chris made my 2 o’clock (csc150°) look much more complicated, by adding 19•360 to it. I modified his idea by adding 42•360 instead for my final product.

Anything you longed to hear?
Nothing in particular.

How can we play with our knowledge of derivatives to create problems instead of solving them?
If we know how to derive, it’s simple enough to work backwards, especially with the power rule. Once we get into rules like chain or quotient, it helps to work backwards by initially creating the thing to derive, then discovering which number you get.

What was most challenging about this “project”?
A number as simple as 1 is remarkably easy to create a derivative for, but said derivative wouldn’t be anywhere near as complicated as this project called for.

Where was your mathematical knowledge pushed?
In newer concepts that I have just learned, such as the chain rule, I understand the very basic sorts of setups, but more complicated elements completely throw me off.

What did you enjoy most about this investigation?
Being ridiculous and tongue-in-cheek with advanced mathematics. That’s not something everyone is able to do (I assume).

Artist Statement

I mainly found the numbers by working backwards. In other words, I created formulas, then derived/looked at the unit circle to find what the outcome would be, and manipulated accordingly (e.g. dividing the outcome by 2, multiplying by 3, subtracting 1, etc.)

November 15 2012

Comparative Essay - Hamlet vs. Rosencrantz and Guildenstern Are Dead

In 1603, a man, probably by the name of William Shakespeare, published a little five-act play called Hamlet. 364 years later, Czech-born Englishman Tom Stoppard also wrote a play, wouldn’t you know it. His play was centered around the Danish prince’s childhood acquaintances, and it was entitled Rosencrantz and Guildenstern Are Dead. Scenes from the first tale are interwoven into the second, as two ditzy playboys wander their way through the metaphysical. These plays are similar in their topics of discussion, yet they differ greatly in their words, words, words.

In one of the million discussions of mortality in Rosencrantz and Guildenstern, Guildenstern says, “Death followed by eternity…the worst of both worlds. It is a terrible thought.” (RGAD p. 72). This is to say that he believes living is definitely better than dying. Hamlet regards life much less fondly, “thousand natural shocks that flesh is heir to” (H act III.i) and whatnot. Rosencrantz and Guildenstern think of life in a brighter light, seeing as they are “the indifferent children of the earth.”(H act II.ii). If nothing else, they have each other…possibly as a substitute for themselves. Gertrude, Hamlet, and even the two men in question have mixed their identities up. Upon introducing himself and his friend to the Player, Rosencrantz says, “My name is Guildenstern, and this is Rosencrantz.” Then, after a brief conference with Guildenstern, he corrects himself (without embarrassment): “I’m sorry-his name’s Guildenstern, and I’m Rosencrantz” (RGAD p. 22). It is not written or interpreted that they are physically identical, so the confusion is not in their appearance. Rather, they are identical mentally. Rosencrantz and Guildenstern - in the Shakespearean play, at least - are the same character. Completely interchangeable. Tom Stoppard’s further exploration into this pair of men leads one to think that Rosencrantz is slightly more knavish. Regardless, these conjoined friends’ relationship with supporting characters is different from Hamlet’s, which affects the light in which those characters are seen.

In Hamlet, the Players are fantastic, Polonius is a scheming dunce, R&G are rats, Hamlet is burdened, Gertrude is…mobléd, Claudius is the devil incarnate, and the rest of the characters are regarded quite neutrally. In Rosencrantz and Guildenstern Are Dead, the Players are the devil incarnate, R&G are more or less helpless, Hamlet is off his rocker, and the remainder of the characters are regarded quite neutrally. The most important relationship of these is the one between the main character/s and the players.

Hamlet has enough faith in the tragedians to declare, “The play’s the thing. Wherein I’ll catch the conscience of the King.” (H act II.ii). He does acknowledge that some actors have “strutted and bellowed that [he had] thought some of nature’s journeymen had made men and not made them well, they imitated humanity so abominably,” (H act III.ii), but he does address them before the play with the understanding that they have the power to make their actions natural and believable enough to evoke true emotion. Guildenstern has a slightly different philosophy.

“Actors! The mechanics if cheap melodrama! That isn’t death! You scream and choke and sink to your knees, but it doesn’t bring death home to anyone—it doesn’t catch them unawares and start the whisper in their skulls that says—’One day you are going to die.’ You die so many times; how can you expect them to believe in your death?” (RGAD p. 83). Guildy doesn’t trust the actors as far as he can throw them. He doesn’t take kindly to lying, and yet he is labelled by Hamlet as a liar, then, as a result, is put to death. Speaking of death, there are definite similarities between the two plays, and dying is absolutely, positively one of them.

Many of the Shakespeare and Stoppard’s scenes are identical in their dialogue, but that’s just too obvious to be true, really. A more major similarity between the Renaissance play and the Mid-century play is that they both mention death, casually and constantly. In the more modern of the two plays, Rosencrantz asks Guildenstern, “Do you ever think of yourself as actually dead, lying in a box with a lid on it?” Guildenstern says no, and Rosencrantz continues. “Nor do I, really…It’s silly to be depressed by it. I mean one thinks of it like being alive in a box, one keeps forgetting to take it into account that one is dead…Which should make all the difference…Shouldn’t it?” (RGAD p. 70). Hamlet has similar qualms regarding Yorick, Alexander, and Caesar. In the graveyard, he says, “Imperious Caesar, dead and turned to clay, might stop a hole to keep the wind away. Oh, that that earth, which kept the world in awe, should patch a wall t’ expel the winter’s flaw!” (H act V.i) They both acknowledge, to varying extents, that dead people are, in fact, no longer living. Ex-people, if you will. Words and actions alike fall to the wayside once humans shuffle off the mortal coil, and all three noble heroes know that. The final lines of a different book entirely, The Great Gatsby, read “we beat on, boats against the current, borne back ceaselessly into the past,” which is terribly fitting to Rosencrantz and Guildenstern’s fatal maritime end. As Guildenstern so fittingly remarks, “Where we went wrong was getting on a boat. We can move, of course, change direction, rattle about, but our movement is contained within a larger one that carries us along as inexorably as the wind and current.” (RAGD p. 122). Being in Elsinore didn’t save Hamlet’s life, because try as he might, he remained on a more metaphorical boat: life. To be not on boats or to not be on boats, that is the question. Living appears as a futile condition nonetheless. After all, each human is just going to turn into spackle as Caesar did before them.

    Multi-century gap aside, Hamlet and Rosencrantz and Guildenstern Are Dead are two sides of the same coin; one theme from two angles. Whether they be bumbling or insane, each main character is an antihero in their own right, and they all have their same quandaries about living and dying. Although these princes and paupers may deal with the quandaries differently, each of them still remain in their one-directional boats, until the end.

November 7 2012

The Problem of the Fortnight two →

October 31 2012

Tidal Wave Project →

October 26 2012

Mindset: Chapters 3 and 4 →

October 16 2012

The Problem of the Fortnight one

Above are the 1st, 2nd, and 3rd patterns of toothpicks. The 1st pattern has 4, the 2nd pattern has 12, and the 3rd pattern has 24. The tasks at hand are to find out how many toothpicks would be in the 100th pattern, and how many toothpicks would be in the nth pattern (i.e. write a formula).

My initial process was to write an x y table, with the pattern number as x and the toothpick number as y, that way, I could try to draw a pattern. In making this table, I discovered that the relationship between x and y was a multiplication that grew by two each time (1x4=4, 2x6=12, 3x8=24), and that the relationships between ys in the growing pattern was decreasing in difference (4x3=12, 12x2=24, etc.). That second discovery didn’t really help me, but using the relationship I discovered between x and y, I was able to find the next few pattern numbers. Then, I focused more on the diagrams themselves. The first one is two rows of one: one vertical, one horizontal. The next is six rows of two: three vertical, three horizontal. The third one is eight rows of three: four vertical, four horizontal. A pattern was falling into place.

Before answering the question of how many toothpicks were in the 100th pattern, I first made a formula:

n(n+1) • 2


1(1+1) • 2

1(2) • 2

2 • 2


2(2+1) • 2

2(3) • 2

6 • 2

12 (correct!)

3(3+1) • 2

3(4) • 2

12 • 2

24 (correct!)

With this knowledge, I was able to discover…

100(100+1) • 2

100(101) • 2

10,100 • 2

There are 20,200 toothpicks in the 100th pattern.

Above are the 1st, 2nd, and 3rd patterns of toothpicks, now with diagonals. The 1st pattern has 6, the 2nd pattern has 20, and the 3rd pattern has 42. The task this time is to find out if I can build a formula off of the one I have just created to accommodate for the added toothpicks.

I created another x y table, this time only noting the relationship between the y sans-diagonals and the y with diagonals. The 1st pattern added 2, the 2nd pattern added 8, and the 3rd pattern added 18. This formula was easier than the last one, especially since I already had the base formula to build off of.

My diagonal formula is…

[n(n+1) • 2] + 2(n^2)


[1(1+1) • 2] + 2(1^2)

[4] + 2(1)

4 + 2

6 (correct!)

[2(2+1) • 2] + 2(2^2)

[12] + 2(4)

12 + 8

20 (correct!)

[3(3+1) • 2] + 2(3^2)

[24] + 2(9)

24 + 18

42 (correct!)

And boom goes the dynamite.

Self-Assessment and Reflection

I learned the all-purpose handiness of x y tables. This whole problem took me less than 20 minutes to solve. I would assign myself a 10/10, because I worked all of this out thoroughly and by myself.

I think I “looked for and made use of structure” (one of the Mathematical Practices and Expectations) because my solution was found primarily through looking at the diagrams. Visual learning is apparently quite significant to me.

September 29 2012

Franny And Zooey Dialectical Journals

Comparative Essay - Franny and Zooey vs. Catcher in the Rye

    Zooey Glass and Holden Caulfield are the protagonists of their respective stories, both of which are written by everyone’s favorite recluse, J.D. Salinger. While Zooey’s story, titled Zooey, is an inward exploration of one’s self in one building, Holden’s story, Catcher in the Rye, is an exploration of New York City while Holden essentially remains himself. At first glance, it may seem as though these tales are entire opposites, but in reality, there are quite a few unmistakable similarities.
    Both boys are firmly rooted in absolutes. To Zooey, you have to be dead to be correct. His absolutes lie in the words of ancient prophecies and his deceased brother Seymour. Although he claims to despise his older brothers, the last piece of advice he gives his younger sister Franny is that you have to “shine your shoes for the fat lady” (FZ p. 201), which is something Seymour told him in their It’s A Wise Child days. Zooey is also not one to miss an opportunity for complement Jesus, saying that he is the smartest man in The Bible because he “realized there is no separation from God” (FZ p. 170). Holden’s favorite prophet is himself, and Mr. Caulfield is quite an  absolute boy. He is constantly on about how “people never believe you” (CITR p. 37) or how money “always makes you blue as hell” (CITR p. 113).
    Zooey and Catcher are similar in a few ways, but this is not to say that they are completely the same. Zooey Glass tells the truth more fervently than George Washington. He is blunt, he is honest, and as a result, he is annoying. In recounting a lunch he had with one of his colleagues, he said, “I can’t even sit down to lunch with a man any more and hold up my end of a decent conversation. I either get so bored or so goddam preachy that if the son of a bitch had any sense, he’d break his chair over my head” (FZ p. 104). Holden has been known to irritate people with the truth on several occasions, but most of the time, he is the kindest pathological liar in the world. While on the train with Ernest Morrow’s mother, he convinced her that her son, the “biggest bastard that went to Pencey”, was the kindest and most popular boy in school (CITR p. 154-158). They both feel remorse, but in the opposite directions.
    Both of these young man in coming-of-age Salinger novels are young, funny, and range between über-philosophical and über-introspective. While they may have opposing social problems (lying too much vs. telling the truth too much), one thing is certain: Holden would hate Zooey. He is an actor, after all.

September 27 2012

Mindset: Chapters 1 and 2

Mindset, a book by Carol Dweck, outlines the ins and outs of two major ways of viewing humanity: the growth mindset and the fixed mindset.

The fixed mindset is the belief that IQ is equivalent to ID; that every aspect of personality and intellect is innate. This mindset pressures those who believe it into proving themselves constantly. Any flat tire is an opportunity to fail or flourish, every grade is a reason to rejoice or bawl. The fixed mindset is very black and white in its values. You’re either perfect or awful (Page 6).

The growth mindset is immensely more open-minded. Although it is acknowledged that people may start off with differing initial talents, the mindset mainly emphasizes the fact that there can always be room for improvement, and betterment is entirely possible. While those with the fixed mindset are stuck in a rut of proving themselves, people with the growth mindset accept their current selves and improve off of what they are (Page 7).

In order to “grow our mindsets”, Carol Dweck asks a few questions, one of which revolves around a past test score, action, or rejection that we believe measured us, then she asks us to take those emotions and put them in a growth mindset (Page 53). I don’t believe that any specific grade or moment has majorly affected or measured me, but there was one bad test score I got in 4th grade that I happen to still remember. I am fully willing to admit that I was quite the slacker in 4th grade, but somehow the grade still took me off guard at the time. It was a C or a D or something horrible like that. I was so humiliated that I hid the test from my fellow classmates before they could ask what score I had received. Obviously, I’ve grown since then. I may or may not have learned from the test score right then, but I did eventually improve my grades quite drastically. I got better, partially because I believed I could.

The most striking element in the first two chapters was the list of all the famous figures who, out of the gate, were nothing special. Tolstoy, Einstein, The Beatles…none of these precious entities were appreciated at first. This is a huge inspiration to keep on reaching towards your goals, and that maybe the “best you can be” is better than you think.

September 19 2012