Free-writing 14 for ENG 1010

It’s a restless life.  I don’t ever really sleep; I’m constantly on call, if you’ll pardon the pun.  The most rest I get is, maybe, eight hours, if I’m lucky, to just hang out on the dresser and recharge my batteries.  But even that gets interrupted every two hours when I have to check for incoming emails.

Don’t get me wrong, I love what I do; I just feel I could be, I dunno, a little more appreciated.  But I know as well as any other cell phone that I’ll probably just be tossed away in two years and replaced by the newer, faster, and sexier models.  I guess that’s why I don’t mind my job so much; it’s a two year contract and then I get to rest forever in that great landfill in the sky.

While I’m still here, however, I feel obliged to give my best.  Occasionally, I’ll hold my ground on an issue, which will force someone to reboot me, and Lord knows there’s nothing better than a fresh start.

Yeah, I field a lot of calls, I mean, I don’t wanna brag, but I can field a lot of calls.  Sometimes I can take multiple calls simultaneously.  I might be a badass by my grandparent’s, “The Landline” standards, but I think it’s pretty standard anymore.

Observation Essay for ENG 1010

He sat down at his computer, situated himself comfortably at the keyboard and began to type.  He got so far as typing his name when a blank, vacuous stare of unoccupied thoughts came over his monitor-illuminated face.  His internal struggle seemed to surface in his efforts to reposition himself; first sitting back and stroking his scarcely stubbled chin, then leaning forward as if to type, only to relapse into the embrace of his chair.

Slowly, he typed out his first paragraph.  He sat and read his first paragraph with a look of deep concentration on his face.  His eyes snapped back and forth with intensity as he read :
“He sat down at his computer, situated himself comfortably at the keyboard and began to type. He got so far as typing his name when a blank, vacuous stare of unoccupied thoughts came over his monitor-illuminated face. His internal struggle seemed to surface in his efforts to reposition himself; first sitting back and stroking his scarcely stubbled chin, then leaning forward as if to type, only to relapse into the embrace of his chair.”

Suddenly, with a burst of enthusiasm he started typing again.  He typed slowly at first, but his typing quickly gained vigor and his vacuous stare evolved to a determined glare.  He paused after nearly every sentence as if to reflect on what he’d just written and perhaps to contemplate what would come next.  He studied his writing, supporting his jaw in his hand, for an over-exaggerated time and then stood abruptly, walked out of his office, grabbed his coat, went outside and lit a cigarette as if to reward himself for writing his first two paragraphs.

He snubbed his cigarette, discarded the butt, gained re-entry to his home, removed his coat, popped open his third and final beer for the night and returned to his desk.  His return to his desk also brought about his return to his words.  He read and re-read what he had written.  His cat joined him at his desk and pleaded for the attention that his paper was getting, pacing back and forth in front of his monitor and doing its best to look adorable.  He barely paid it any attention but was obviously inconvenienced by the attempt to type with a fifteen pound addition of fur in his lap.

After being ignored for what must have been, for a cat, a seemingly endless entirety of five minutes, the cat fled his lap in search of attention elsewhere.  He resumed his writing in a determined, yet cautious manner, pausing between ideas as if to verify their accuracy.  His movements, appearing awkward and self-comforting in nature, gave the impression that he was still struggling with some internal ideas, or that maybe he wasn’t entirely comfortable with the subject of his writing.
 
This pulsing “start writing”, “stop to contemplate” pattern continued for some time which caused the quantity of his writing (barely two pages at this time) appear a belaboring process.  His freshly poured beer, largely ignored, began to perspire as if mocking his struggle.  Occasionally, he would break from his process to reference a word on the internet.  He would navigate to Thesaurus.com and type in words like, “burden” or “seem,” and then return to his paper and use an appropriate synonym.

After every paragraph, he would sit back and re-read his writing in its entirety.  Nearing the end of his second page, he perused his words cautiously.  His vacuous stare returned as he attempted to type further, his hands resting on his keyboard as if anything could startle them into typing again.  He sat in this position for a few minutes, then with a sigh of defeat, he stood, looked at his cat begging for attention on the floor, and mumbled, “Next time I’ll come up with a subject to observe, kitty.”  He picked up his cat, stroked its back and continued, “Observing yourself while you type your observations is exhausting.”

He left his computer with another sigh.  His shoulders sagging and with a perplexed stare; he studied his ignored beer before grabbing the glass, downing the liquid and going to bed.

I Remember: First Drive for ENG 1010

I have a somewhat diverse, maybe even unusual, experience with cars.  When I was a child in Sacramento, probably no more than six years old, my father would let me sit on his lap and steer our white mini-van down a regularly unoccupied stretch of road.  Little did I know my father’s hands were always at the ready to re-assume control of the vehicle should we veer off course.  However, to my parent’s dismay, the power and control I felt at the wheel of that van, combined with my ambitious nature, would later prove to be incorrigible.

When we moved to Wyoming, there was a different attitude towards driving.  Driving begins at fourteen for most kids in Wyoming.  Due to the vast stretches of farm land and long commutes to schools, most kids get their farmer’s permit, which allows them to drive, legally, at fourteen.  I was convinced that I was in desperate need of my farmer’s permit, even though we lived in town and our house was nothing like a farm.  My parents didn’t share my outlook.

I had one friend, in particular, who lived on a large expanse of land.  I would regularly visit him and we would drive his beat-up old automatic transmission, orange Jeep Cherokee, with absolutely no suspension, around the sagebrush flats at the base of the bentonite hills.  Since there were no roads and no police, we often demanded more of the Jeep than it was designed to give.  We would barrel through large sagebrush, build jumps, do donuts, climb steep hills, and engage in regularly irresponsible and dangerous activities.  The Jeep was probably only on four wheels when it was at rest.

Confident of my driving skills, and perhaps to spite my parent’s disapproval of a farmer’s permit, one night, while my parents were away, I decided I would take our mini-van for a spin.  I was certain I could drive around for a while before they got home.  Unfortunately, I didn’t understand the mechanics of a manual transmission.  I figured out how to back the van out of the garage and into the street, but I couldn’t figure out how to drive the car forward.  Hardly fazed, I proceeded to drive the van, in reverse, around my neighborhood for some time.  I was at the bottom of a large hill, when I realized that I would need to park the van back in the garage, which would require a forward direction.  Realizing I was running out of time before my parent’s return, I parked the van at the bottom of the hill, ran to my house, picked up my phone and called my older friend who definitely knew how to drive a stick.  He laughed hysterically at my predicament, but agreed to come help me.  We got the van back in the garage and resumed our normal routine, so as not to exhibit our guilt upon my parents return.  I’m not sure if my parents ever found out about that endeavor.  In retrospect, I’m not sure how I figured out one direction but not the other. 

It was about two years later that I passed my exam and received my learner’s permit, which allowed me to drive, legally, in the company of an adult.  My dad drove our little, red, two-door, gutless, manual transmission, Geo Metro out to a dirt road outlining the base of the foothills near my house.  This was my first, legal, driving experience, although by this time, I’d had plenty of driving experience and had figured out how to drive in both directions with a manual transmission.  We began with a few starts and stops to get the feel of the clutch.  We then proceeded to barrel down the dirt road.  For some reason, I felt the need to hold a perfect speed.  With my eyes focused on the speedometer, we nearly veered off the road a few times before my dad asked me what I was doing.  I told him I was trying to hold the speed.  He laughed at the idea and told me that staying on the road was more important than the speed at which we drove off the road.  Eventually, I won the approval to occasionally drive the family cars, only with the presence of an adult, of course.

In Wyoming, being able to drive is invaluable.  When I moved to the metropolis, my driving seemed to contribute to the already congested roads and I began to prefer my bike and my feet, which I found to be much more reliable, safe and cost-effective transportation.  I still enjoy attempting to drive; I just don’t like competing with other people’s attempts.

Observation: Something Weird for ENG 1010

On my walk from the light-rail to work, I generally walk up 14th Avenue, past the State Capitol.  Sherman Street crosses 14th and becomes the entrance to the parking lot at the Capitol.  There are two gates that must be raised to enter either the West or East parking areas around the building.  Before the gates, there is a small circular area where vehicles tend to drop people off or just turn around.  Last Friday, I was on my regular walk up 14th Avenue when I arrived at Sherman Street.  I had intended to walk past the Capitol as usual, but this day there was an RTD Handicap Bus blocking my route up 14th Avenue.  I stood by patiently as the bus attempted to turn around in the tight area between the two gates.  The bus pulled forward toward the Capitol, and then backed up toward 14th Street.  Unsatisfied with her first attempt, the driver repeated this maneuver but did not stop at an appropriate distance from the pole supporting the traffic lights.  Instead, she backed the bus, backed some more, and then just kept backing until there was a loud “crunch.”  I was standing close enough that the sound caused me to jump back in a futile attempt to protect myself from any flying debris.  Upon pulling forward, it was extremely noticeable that the bus had dislocated a pedestrian walk/don’t walk light and, were it not for the wires holding it to the pole, this light would have landed on my foot.  The weird part is what happened next.  A city owned bus, operated by a city paid bus driver, who just destroyed city property, somehow suddenly figured out how to turn the bus around and tore out of the Capitol parking lot in a hurry, the passengers bouncing and swaying in response to the busses over-exaggerated movements.  I stood in admiration of the irony as I watched the bus disappear into the city streets, the pedestrian light swinging, pendulum-like, by its dangling wires.

Round-robin writing 2 for ENG 1010

I am psychologically kind of a moron.  Really, I'm really dumb.  Although I'm aware of my idiocracy which is sort of contradictory to my statement.  So, maybe I'm not as much of a moron as I make myself out to be.  But I digress...

Suddenly, I had an epiphany which as a moron is quite a feat; my stupidity is a direct result of my mental attitude.  So I began to enrich my life with literature.

Meanwhile, I find my self enjoying topics that I've never considered before.  I am enriching my self with new topics and in doing so, I find a sense of self-actualization, and thus, begin to credit myself.

The point I'm trying to make is literature is good, being a moron is bad.

Round-robin writing 1 for ENG 1010

This is my first post of round-robin writing.  We are given a starting statement and asked to write freely for a given amount of time.  At the end of that time, we pass our papers to a group member, read what was previously written, are given another starting statement and then continue the story.

Once upon a time, there was Shirley.  Shirley disliked time, so she got off it.  Timeless existence was much more suited to Shirley.

Without warning, Shirley was bombarded with thousands of clocks falling through her ceiling.  She was severely injured.

Turning in the direction of timelessness, Shirley realized she could get no help there because there were no doctors on the clock.  With a heavy heart, Shirley started back towards the land of time.

The reason I told you all of this madness was to show that time is somthing out of reality.  It's a mere idea, we cannot see it, or hear, or touch it.  But what is reality is a fluffy rabbit named Rufess.  Boom!, That's reality!

Free-writing 13 for ENG 1010

Meanwhile, back at Jessie's Place, I finish my third Bud, order my fourth.  Now, I tell myself, my courage bolstered by booze, I'm ready to wear that dress.  I'm not usually a fan of dresses, but the beer rendered me indifferent.

I undress to the sound of Jessie's laughter and drunkenly step into the dress one foot at a time.  My equilibrium impaired, I fall on my face as soon as the dress is at my knees.  This causes Jessie's laughter to increase to the point that she's seemingly suffocating.

I attempt to lift my weight off the floor, but just then, her dad walks in.

Free-writing 12 for ENG 1010

With a smash of my hand, the potato chips are reduced to a pulp, and I feel the cold lump of the lip beneath my fist.  I clasp the bag shut and shake it hard in an effort to ensure chip coverage in all the nooks and crannies of the lip.

I'm not sure what compelled Donnie to wear a potato chip bag on his face all day, but after five hours of mumbled speech, he deserved that punch in the face.

I ask Donnie to remove the bag, but he shakes his head violently, which cases chips to fly everywhere.

Free-writing 11 for ENG 1010

I have several friends from Hawaii and all of them are crazy.  I'm not sure if it's the constant sun and salty sea-air, or maybe it's the isolation of being on an island.  Whatever it is, they're all batty, and that's what I love about them.  I've been to Hawaii once, but only stopped on a layover to Japan.  I didn't see much of the island state, but the stories my friends tell me are enthralling.

Just once, I'd love to walk the crusted lava plains, climb the active volcanoes, swim the whale infested channels, relax on the black sand beaches, or crack my own freshly picked coconut.  From what I understand, the smaller islands are like small communities, or tribes, where everyone is friendly and welcoming.

Free-writing 10 for ENG 1010

There once was a horse named Jerome.  Jerome was a different horse, or at least, he felt different.  Most of the other horses wouldn't let him play with them just because he had toes.

Now, most horses are proud of their clompy hooves and one of their favorite games is "Clomp the Loudest", which is when they all stomp their feet to see who can make the most noise.

Jerome was terrible at this game.  Being genetically engineered as a cross between a horse, a frog, and a pigeon, Jerome's webbed feet made more of a "smack" than a clomp.  His light bird-bone structure didn't help either.

Free-writing 9 for ENG 1010

"There are three reasons why I think gravity is stupid, but I don't want to bore you with my hatred of such trivial things." said Sam.

Mary regarded him quizzically and asked, "If you hate gravity so much, why don't you just become an astronaut?"

Free-writing 8 for ENG 1010

"I don't remember!"  I exclaimed, blood pouring down my face and mixing with the rain which was falling in an oppressive manner.

"How can you not remember?" asked a lady looking at me, her face full of confusion.  It was then that I realized I too was confused.  I had no idea who this lady was, when it started raining, why my face was bleeding, where I was, and who's shirt was this on my head?

The lady continued, "Well, do you want me to call and ambulance?  You're bleeding pretty bad there."

"Where am I?" I asked.  Once again, the lady looked confused.  "How did I get here?"  I asked again.  The lady stared at me in disbelief and started reaching for her cell phone.

Free-writing 7 for ENG 1010

"If you think fixing light fixtures will fix this problem," said his mother, "well, then, you've got something else coming."  Sammy stammered, "But... but..."  "You're gonna need more than a little extra light to get yourself out of this mess." interrupted his mother.

Sammy stood on the ladder blankly staring at his mother and waited until she was done verbally berating him.

Free-writing 6 for ENG 1010

His mother came running out of the house.  She waved us down in the car as we approached.  We pulled over and rolled down the window, which is when we saw the look of terror on her paling face.

"What's wrong?" asked dad.

Suddenly, his mom fainted.  "Call the Ambulance!" dad exclaimed as he exited the vehicle.  I reached for my phone and dialed 9-1 when I noticed the car was rolling back down the long dirt road.

Free-writing 5 for ENG 1010

"There are many reasons why."  I said.  "Name one."  she retorted.  "Well, one might be because it's physically impossible."  She questioned, "Impossible or improbable?"  "Touche," I said, "I see I've met my match in physics."  "Perhaps," she replied, "but before we get into that, I want to hear another reason."  "Okay," I said, pausing to think, "Well, I dunno, I can't think of anything.  I just can't grow a mustache and that's the way it is."

Free-writing 4 for ENG 1010

The computer screen was blue.  I asked Josh what it meant.  "Oh man!" he said excitedly.  "Oh, man!" He said again with a giggle.  "Oh, man, ohman oman!" he repeated, his giggle turning into maniacal laughter.  I sat and watched his odd performance, glancing at the screen occasionally to see if it had changed.  When the laughter started subsiding, I looked carefully at Josh and asked if he was on anything.  "No, I just haven't slept in about four days."

Free-writing 3 for ENG 1010

Only a few more yards to go and I would be safe.  I struggled with the weight behind me.  Only a few more yards and I'd be the best, I'd hold the record, I'd win the medal.  Only a few more yards and this burden would move under its own momentum.  Only a few more yards and I can let off this tension.  Only a few more yards and I'll have the title of Strongest Man in the Universe.  This semi-truck sure is heavy.  Wait, why am I doing this?  Oh, who cares, look at my beautiful muscles glistening with sweat!  I'm almost the manliest man in man's existence.

Free-writing 2 for ENG 1010

The waitress stood tall.  The man at the table in front of her said, "You sure do stand tall."  The waitress looked at him with a glare that could melt iron.  "Why must you always come here and point out my physical features?!  I know I'm tall.  My parents were tall, my grandparents were tall, it's genetic." she said with a matter-of-fact tone.  The man replied, "Geez, sorry.  I was just trying to make conversation.  Besides, you have remarkable features worth, err... remarking on."  "Here's your drink." said the waitress dropping a sweaty glass with a light brown liquid inside.  She then stormed off with a little more of a slouch.  The man sat quietly at his table sipping his long island iced tea and thinking of warmer weather.  When the waitress returned, the man apologized and asked, "Would you like to come with me to Acapulco?"

Free-writing 1 for ENG 1010

This is my first of many free-writing posts.  In class, we are given an opening statement and from that, we write freely for a given amount of time.  We are asked to write as quickly as possible.  Nothing is restricted and free thought/writing is encouraged.

The doorbell rang, the dog barked and Frank struggled to restrain the dog from barging out the door.  Luckily the screen was shut, but nevertheless the mailman was petrified and white as a sheet.

"Sorry about that." said Frank, but the mailman didn't budge.  The dog continued to pull against Frank's restraint and bark as though the mailman had just murdered its mother.  Frank did his best to subdue the dog and at the same time, tried to communicate to the mailman to just leave the box at the door.  Still no movement from the wide eyed and terrified mailman.

Observation Paragraph: Eating - for ENG 1010 - Freshman Composition: The Essay

In a misleading manner, a large man with a stocking cap daintily held a limp fry between thumb and index finger, pinky waiving in the wind.  The man, talking to his friends, whipped his fry to and fro while the flaccid fry lagged behind.  The man consumed the fry in no less than two bites.  No ketchup, no mustard, just fried potato meeting its brutal end by tooth induced hemicorporectomy.  In a complete departure from his delicate fry eating etiquette, the man picked up half of his cheesesteak.  The man’s eyes widened as he sized up sloppy sandwich.  Much like a snake, the man seemingly dislocated his jaw and it appeared that he would swallow his victim whole.  Just before the entire twelve inch sandwich had entered his mouth, the man’s jaw snapped shut, his teeth severing bread and meat in one jolting movement.  The force of his bite sent molten cheese flying into his face, across the table and into the face of his companions as well.  Mouth filled to capacity, cheeks bulging in glutinous delight, the man tried, unsuccessfully, to chew and giggle at the same time.  His giggle caused a breach in the vacuum of his mouth and a small strip of gray beef slipped out from between his lips.  In an attempt to rescue the AWOL meat, the man used his index finger to force the meat back in with its peers.  As if to secure the meat in its rightful place, the man somehow managed to fit a straw between his lips and slurped his soft drink.  The man chewed laboriously and slowly and eventually his rotund cheeks returned to their natural position, though they were now forming beads of sweat.  Only after swallowing his mouthful, did the man attempt to wipe the spattered cheese from his face.  Then the man took another bite.

Admiration Narrative - Final Draft (changed subject) for ENG 1010 - Freshman Composition: The Essay

I remember being excited to be a part of nature.  My family decided to move to Wyoming where my father got a job as a pastor in the small town of Greybull.  Before the move, some of the church members sent me some books on the topic of Wyoming.  All of them were books about the indigenous animals.  I found quickly that Wyoming was nothing like I had imagined.  Much like the residents of Southern California rarely visit the Pacific Ocean; Wyomingites rarely took notice of the wildlife unless hunting.

Throughout my school years, I spent some time exploring the wilderness surrounding our small town.  Usually alone, I would let my curiosity lead me over the vast expanses near my house.  I longed to explore the nearby mountains, but aside from feet and a bike, I lacked the transportation to get there.  I often found myself within a half day’s walk of home and alone with my adventurous spirit.

Mark was a man in his late twenties from California with unremarkable features and a black Jeep.  I was about 14, just on the cusp of driving but starting to submit to the disinterested ways of the locals.  Mark visited our church in Greybull and after church one summer day, approached me and asked if I would like to join him on a fishing trip.  I was taken aback at his apparent disregard of the adult-child social guidelines but I received permission from my parents and accepted his invitation.

We boarded his uncovered jeep and departed the church parking lot.  “I’ve wanted to find some good fishing spots on the mountain,” confessed Mark, his anticipation nearly boiling over.  “I’m hoping you can help point me in the right direction.”  I was flattered that this man was so excited to seek the advice of me, a lowly fourteen year old boy with little fishing experience and even less confidence.  “I’m not sure I can help.” I said nervously.  “You know where there’s water, a lake or a river or something?”  Mark asked.  “Well sure, but…”  “Then you can help!” Interrupted Mark with confidence.  “I’ll need to go by my house to get my fishing equipment.”  Mark looked at me and then reached behind my seat to lift a handful of fishing poles.  “I’ve got plenty of equipment.” he said, “You can just use mine.”  I nodded in agreement and we continued down the highway in silence.

The Big Horn Mountains make their presence first known when you cross the Shell Creek Bridge and enter a labyrinthine canyon.  Mark and I approached the canyon in his Jeep and I told him about a fishing spot just under the bridge.  He ignored the comment and continued up the canyon.  As we twisted and climbed the steep canyon roads, I would point out spots that I’d fished but we just kept driving.
 
Mark slowed the jeep at the point where the road and creek go their separate ways.  “How’s the fishing up there?” He asked, pointing at two muddy tire tracks continuing upstream.  “I don’t know.  I’ve never been up that way.”  I replied.  “Well then, that’s where we’re going!” Mark declared excitedly, gearing his jeep into four-wheel drive.  Before I could voice the need for caution, we were bouncing down the tire tracks, flinging mud into the back of Mark’s Jeep and nearly everywhere else.  We travelled slowly and sloppily for what seemed like hours before Mark stopped the Jeep.  He looked at me and asked, “Do you know where we are?”  “I have no idea.” I confessed.  “Perfect!” Exclaimed Mark, “Let’s fish!”
We pulled out all of the fishing equipment and walked another mile upstream before I noticed the fishing poles we were carrying.  I’d done my fair share of lake, stream and pond fishing, but I’d never been fly-fishing before.  I confessed my ignorance to Mark, but he assured me that I would be a great fly fisher and he would help me out.

We sat on a rock and Mark showed me how to attach the fly to the fishing line.  We both pounced rock-to-rock toward the center of the frigid creek.  I watched as Mark flicked his wrist causing the fly to whip back and forth on the end of the line, before landing serenely on the water.

Mark looked at me and, so as to not startle the fish, whispered; “Now you try.”  And try I did.  I attempted to imitate Mark’s movements, but mine seemed more violent.  Mark motioned for me to stop trying and came closer to whisper, “Don’t just throw the fly into the water.  You need to believe you are the fly.  You need to make yourself look as delicious as possible to those fish.  You need to think like a fish and a fly and a fisherman all at the same time.”  I was reminded of the cliché kung-fu movies I had seen before.  “You cannot break the board if you are not one with the board.” They would say.  Mark’s idea struck me as somewhat silly, but I figured I would try it.  I reeled my fly back in, pulled out some line and again violently shook the pole and slammed the fly into the water.  “Try again.” Said Mark, “And try to relax, we’re here to have fun not to be perfect.”  Again, I thought the remark was slightly odd, but I tried again.  This time the fishing line waived through the air with a graceful curve, the pole flexed to and fro with a flux in step with the line, and the fly plopped delicately on the water.  Almost immediately, there was a tug on the line.  I waited… another tug.  I waited again, this time returning the tug of my submersed opponent.  I reeled the line in to find a tiny two-inch fish on the end.  Mark caught the look of disappointment on my face and started to laugh.  “Well at least you caught one, and that was a really good cast.”  He chuckled, “See, I told you you’d have no problem picking it up.”  We threw the fish back.

We fished the rest of the day without catching a single fish.  I was disappointed but Mark pointed out that we had a great day regardless of our catch.
  
Mark and I went fly fishing several more times before he left Greybull, though we never caught any more fish.  Throughout our fishing together, we both got to explore new territory, interact with nature, and try new things.  I learned to fly fish, but more importantly, I learned how to relax and enjoy the journey and then accept the end of that journey, be it "failure" or "success." I learned that friendship doesn’t necessarily have boundaries, age or otherwise.  I learned to never abandon my adventurous spirit.  I learned how to appreciate and view my surroundings from a new perspective.  I learned to think like a fly and a fish and a fisherman at the same time.

CAP1 for MTH 1610 - Integrated Mathematics I

In this problem we are asked to find the dimensions and volume of a box folded from an 8.5 x 14 piece of paper.  We are then asked to find the largest volume by assigning a variable to one of the dimensions.  In the following five part process, we will figure out how to solve these problems:

Part 1 - Area

To solve this problem we must first understand area.  Area is the measure of the span of a two dimensional surface.  For example, let’s say the surface we are working with is 3 inches wide and 4 inches long.

If we were to measure and draw lines both vertically and horizontally every one inch, we would have a grid with a series of 1in x 1in squares.  The amount of squares in this grid would represent the area of the entire surface in inches².  If we counted the squares, there would be 12.  So this rectangle has an area of 12 inches².

To reduce the time of counting individual squares, we could say that we have 3 rows composed of 4 units.  So we could add 4 units together 3 times (4units in row1 +  4units in row2 + 4units in row3)

        

or (4+4+4).  4+4+4 has a sum of 12, which is how many squares we counted originally.

To further reduce the time of adding, we can multiply.  Since we are adding 4 units 3 times, we can say 4x3 = (4+4+4), or equally, 3x4 = (3+3+3+3).  These problems also have a sum of 12.

In our case (rectangle), we can say that area is the number of rows multiplied by the number of columns, or width x length, or base x width.  This formula will always equate to the number of squares on your grid, no matter the unit of measure (as long as they’re the same for base & width) and no matter the size of the rectangle or square.

Part 2 – Volume

Volume is area but with an added third dimension: height.  In our example problem we had a 3x4 rectangle.  If we added a third dimension, say 2 units high, our rectangle has now become a rectangular prism. 

Since we are measuring a third dimension, our unit of measure must also gain a third dimension.  Our 1in x 1in square will now become a 1in x 1in x 1in cube.  Volume will measure the amount of these cubes that will fit into our rectangular prism (or box).

Since our box is 2 units high, we can find the volume by first finding the area (base x width = 12).  2 units high is like saying we are going to stack 2 boxes with an area of 12.  We can add the two areas (base x width) + (base x width) = 24.  If we count the number of 1in cubes that fit into our box, we would count 24.

If the height changes to 3, we would need to add the area 3 times: (base x width)+(base x width)+(base x width).  Instead of adding all of these, we can use the shortcut of multiplication and say: base x width x 3.  Since 3 is our height, we can adjust this formula for use with any box, cube or rectangular prism of any width, base or height as the formula: base x width x height = volume.

Base = 4, Width = 3, Height = 3 .  Base x Width x Height = 4 x 3 x 3 = 36.  A height of 3 = 36 cubes. 

Part 3 – Finding measurements between the folds

In our problem, we are asked to find the dimensions and volume of a box folded from a 8.5 in x 14 in piece of paper.  Using our formula for area (base x width), we know that the area of this piece of paper is 119. Base of 8.5 x Width of 14 = 8.5 x 14 = 119. 

However, since we are folding the edges of this area to create height in the third dimension, our base area will decrease as our height increases.  In our problem, the height is 3, so we will fold 3 inches from each edge to create height. (Highlighted yellow will become height, green is remaining base area).

       

This also means we need to remove each fold’s measurement from our base area (see above green area remaining after folds).  In this case we will remove 3 inches from both sides of the 8.5 inch width.  Since our paper is folded in half, the middle 3 inch fold will become the wall height between the base and the top, making the remaining (green) areas our base and top.

Now that we know where the folds are, we can find the area for our base and top. We can use our original measurements of 8.5 x 14 to find the new measurements of our base and top.  Our base would be 8.5in minus the 3in folds from the bottom and top.  If we add the fold measurements from bottom and top we get 6in, or 3in x 2.  8.5in – 3in – 3in = 8.5in – (2 x 3 in) = 8.5in – 6 in = 2.5in.  So we can say our base has a width of 2.5in.

Likewise, we need to subtract the folds from the base area for the length.  However, since we are folding the paper in half, our starting base length is 7in instead of 14in (14/2 = 7).  Also since the center fold is the beginning of our wall, it is also the end of our base, meaning we only need to subtract the first 3in fold from our 7in length.  7in – 3in = 4in.  So our base has a length of 4 in.

Now that we have the measurements for our cube (Base = 2.5in, Width = 4in, Height = 3in), we can find the area of our base using our formula (base x width).  4in base x 2.5in width = 10in² (our answer is squared, because we are measuring how many 1in squares(²) fit into the area).  So our base has an area of 10in².  If we find the measurements for our top (using the same methods described above), we will see that it also has an area of 10in².  Our problem gives us a height of 3in and our folded walls measure 3in.  If we plug that 3in height into our (b x w x h) formula, for volume we get: 4in base x 2.5in width x 3in height = 30in³ (our answer is in inches cubed(³) because we are measuring how many 1in cubes fit into the box).

Part 4 – Using a variable and universal formula.

We now know that our box has a volume of 30in³.  Is this the optimum volume?  In order to find the answer to this, we must create a variable in our formula and reconfigure the formula to account for this variable.  In this case our variable will be height.  We can call our variable “X”.

We know that volume is base x width x height.  If we add our variable for height, we can say our equation is base x width x (X).

We can also account for our folds changing the size of our base area.  We know that width is originally 8.5in and that there are equal folds on both sides which will reduce the width of 8.5in.  Since the folds will become height (our variable “X”) we can say: width = 8.5-2X.

So far, our equation for volume now looks like this: (base)(8.5-2X)(X), which still follows our original formula (base)(width)(height).

Our base of 7in (because the 14in paper is folded in half) also decreases with one variable (“X”) fold, so we could say: base = 7-X

Now our equation looks like this: (7-X)(8.5-2X)(X) = Volume.  We can test this equation by solving for a volume we already know.  In our original problem, the variable height (“X”) was 3in.  If we replace all of the “X”s in our equation with 3s, we should come up with the same answer as before.

(7-3)(8.5-2x3)(3) = Volume

(4)(8.5-6)(3) = Volume

(4)(2.5)(3) = Volume

(10)(3) = Volume

30 = Volume  = the same answer as our original problem

Part 5 – Applying the Formula

Now that we have our formula, (7-X)(8.5-2X)(X), we can begin our quest to find the largest volume.  There are several methods to quickly resolving this issue.  My preferred method is estimation mixed with logical elimination.

We have attempted solving the equation with 3 as our variable, so we can safely eliminate 3.  But what if we tried 4 or 2?  Let’s try both.

(7-4)(8.5-2x4)(4) = Volume

(3)(8.5-8)(4) = Volume

(3)(0.5)(4) = Volume

(12)(0.5) = Volume

6 = Volume

(7-2)(8.5-2x2)(2) = Volume

(5)(8.5-4)(2) = Volume

(5)(4.5)(2) = Volume

(10)(4.5) = Volume

45 = Volume

Our variable of 2 has resulted in a significantly higher volume.  So let’s continue down that path and see what happens when our variable is 1:

(7-1)(8.5-2x1)(1)

(6)(8.5-2)(1)

(6)(6.5)(1)

(6)(6.5)

39 = Volume

Now we know that the variable 1 has a volume of 39, the variable 2 has a volume of 45, and the variable 3 has a volume of 30.  Since 39 and 45 are both larger amounts than 30, we can logically estimate that the largest value will be somewhere between the variables 1 and 2.  So let’s inspect this theory and split the difference to see what we get with the variable 1.5:

(7-1.5)(8.5-2x1.5)(1.5)

(5.5)(8.5-3)(1.5)

(5.5)(5.5)(1.5)

(30.25)(1.5)

45.375 = Volume

45.375 is greater than 45, so we know that the variable 1.5 results in a larger volume than both 1 and 2.  Now we can try either side of 1.5, let’s try the variables 1.25 and 1.75:

(7-1.25)(8.5-2x1.5)(1.25)

(5.75)(8.5-2.5)(1.25)

(5.75)(6)(1.25)

(34.5)(1.25)

43.215 = Volume

(7-1.75)(8.5-2x1.75)(1.75)

(5.25)(8.5-3.5)(1.75)

(5.25)(5)(1.75)

(26.25)(1.75)

45.9375 = Volume

Since the variable 1.75 yields the largest volume of 45.9375in³, we can say that 1.75in is the optimum height for our box to a quarter of an inch.

If you feel a need for more accuracy, we can continue trying smaller and smaller fractions of an inch, until eventually we would reach a 1.71in variable which would yield a volume of 45.953172in³.  1.71in would be the optimum height value to 1/100^th of an inch. 

(7-1.71)(8.5-2x1.71)(1.71)

(5.29)(8.5-3.42)(1.71)

(5.29)(5.08)(1.71)

(26.8732)(1.71)

45.953172 = Volume

However, the variable can still be broken down further to 1/1000 of an inch, 1/10000 of an inch, and so on.

If we took all of our variables and plotted a graph for volume, we would see that the graph peaks at 45.953172 and drops on either side of that optimum volume.

Part 6 – Conclusion

Now that we have gathered all of our data, we can answer the original questions:

Question:

What are the dimensions of a 8.5 x 14 inch paper folded with 3 inch sides to create a box?

Answer:

·         8.5in – 6 in (2x 3in folds on top and bottom) = 2.5in.  So we can say our base has a width of 2.5in. 

·         7in – 3in (1x 3in fold on left) = 4in.  So our base has a length of 4 in.

·         And we are given the height of our folds:  3in

Our box has the dimensions 2.5in x 4in x 3in.

Question:

What would its volume be?

Answer:

·         Volume = Base of 4 x Width of 2.5 x Height of 3 = 4x2.5x3 = 30

Our box has a volume of 30 inches³

Question:

Describe how to determine the dimensions of the box without actually building and measuring it.

Answer:

·         Base = (7-3)

·         Width = (7-2x3)

·         Height = (3)

(7-3)(8.5-2x3)(3) = Volume (see Part 4 above for explanation)

Question:

Describe how you determined the volume of the box

Answer:

·         See above answer and Part 4

Question:

Find the largest volume possible with a variable height

Answer:

·         (7-1.75)(8.5-2x1.75)(1.75) = (5.25)(8.5-3.5)(1.75) = (5.25)(5)(1.75) = (26.25)(1.75) = 45.9375in³ = Volume.  This is the largest volume using quarter-inch increments for the variable height.

·         (7-1.71)(8.5-2x1.71)(1.71) = (5.29)(8.5-3.42)(1.71) = (5.29)(5.08)(1.71) = (26.8732)(1.71) = 45.953172 = Volume.  This is the largest volume using 1/100^th inch increments for the variable height.

·         See Part 5.

All illustrations by Matthew Henderson using Adobe Illustrator.  Source files available upon request.

All graphs by Matthew Henderson using Microsoft Office Excel – Original Graphs and Data Sheets attached.

I Remember My First Best Friend for ENG 1010 - Freshman Composition: The Essay

Being a military family, we moved frequently.  Our moves were less neighborhood-to-neighborhood and more country-to-country.  This instability made it difficult to make lasting friendships.  My father eventually took reserve military status which allowed my family to settle in one place for an extended period.  We settled down in Sacramento, which is where I met Mikey Stanton, my first best friend.

Having recently graduated from seminary school, my father started a small church in Sacramento that met at a local college campus.  It took a while for the population to grow, but eventually there were several families in attendance, the Stanton’s being one of them.

After church, Mikey and I would roam the vacant college buildings, playing hide-n-seek, tag, freeze-tag, racing and occasionally making up our own games.  We would play and explore for hours and do our best to hide from our parents or pretend we didn’t hear them beckon when it was time to go, anything to extend our play time.

Eventually we began visiting each other’s homes.  We would play Sega Genesis, Transformers and G.I. Joe at the Stanton’s house and Ninja Turtles, harass my sisters, and attempt digging to China at mine.  LEGOs, Cartoons, and Soccer were played regardless of where we were.

Mikey and I attended different schools.  When school was in session, our friendship would slowly dissipate as we explored new and different friendships.  However, every summer, our friendship would re-kindle in full.

In fourth grade, my dad received a job offer in Wyoming.  We packed our things, loaded up a moving van and left.  Of all the things I left behind, I distinctly remember Mikey Stanton being the most difficult.