The College Football Trophy Room: Week 1

Enjoy this week's installment of my series on the trophies found in college football. If you need an explanation of the series you can read the introduction. Previous editions in the series are archived under the "trophy room" tag.

The Blue Ribbon Trophy of the Week

Above: A  photo of the most West Virginian trophy ever. Taken from GoHerd.com

Friends of Coal Bowl Trophy- Marshall Thundering Herd vs. West Virginia Mountaineers- 9/1/2012 
To start the season, I want to focus on a trophy that may enjoy it's final Saturday in the sun for quite some time this week. West Virginia has two teams that compete in FBS-level football, so it would seem natural for the two to play every year. Yet this Saturday marks only the twelfth time the two have met. It will also be the last time the two teams play for the foreseeable future. So to commemorate the occasion I would like to share a little information about the Friends of Coal Bowl Trophy. 

The trophy was conceived as part of package to fire up a rivalry between the Marshall and WVU. The arrangements for the series had to be negotiated by West Virginia's governor at the time (college football being one of the most pressing issues facing the chief executive of any state). A series of games was scheduled to begin in 2006, and a suitable prize had to be made. For a game between West Virginia schools, the trophy had to cram as much West Virginia stuff into one physical object as the laws of physics would allow. You start with a carbon base from Clarksburg, WV. Then you add a face plate made in Charleston, WV which has been engraved at Alum Creek, WV. After that go to Williamstown, WV, so a glass blower can shape you an ornamental trophy shaped like a football. Next dig up some coal from the state's largest coal seam in Scarbro, WV. Take that to Amsted, WV to liquefy it. Finally you pour the coal inside the glass football to create a trophy that's so Appalachian it should be the subject of a Loretta Lynn song,

All of that seems like the sort of thing that should inspire a wave of provincial pride that draws all West Virginians together. However, the Friends of Coal Bowl has drawn controversy from multiple quarters. Some want to see this trophy retired because it has never changed hands. In fact Marshall has never defeated West Virginia on the gridiron. In 1997 the Thundering Herd even had Randy Moss and still couldn't win -actually after Super Bowl XLII that's not so surprising. So it can hardly seem like a rivalry if the WVU janitor never has to unlock the trophy chest. Even if Mountaineers were forced to surrender the hardware, some still feel the whole thing is too contrived to last. A rivalry has to evolve as the natural product of repeated contests and steadily increasing animosity between the two organizations. 

Setting aside questions about a competitive mismatch, political controversy has tainted the Friends of Coal Bowl. (You have no idea how many times I've tried to type either "cowl" or "boal" while writing up this blog post.) Critics have found it distasteful that an openly political organization like Friends of Coal was awarded naming rights to the game, without so much as a competitive bidding process. Though I cannot come up with any institution that would want to be associated with a sporting event in West Virginia more than the coal industry, with the possible exception of John Denver's estate. This has led others to use the game and its associated trophy as examples of some sort of corrupt political process. It gives the impression that this trophy game exists solely to allow various power brokers to curry favor with each other. In response, I say that there are lots of unsavory things power brokers do to curry favor. At least this time the rest of us got a football game and a unique trophy out of it.

Spoils of the Game- Week 1
This is where we take a look at all the prizes at stake in this week's games.

Above: The winning team in the Rocky Mountain Showdown gets to hoist the Centennial Cup, from ColoState.edu

Centennial Cup- Colorado University Buffaloes vs. Colorado State Rams- 9/1/2012
No collegiate sporting event in the state of Colorado draws more fans than the battle between the Rams and the Buffaloes for the Centennial Cup. The trophy owes its name to the nickname for the state of Colorado, The Centennial State. That nickname arose because President Ulysses Grant thought a good way to mark the USA's 100th birthday was to admit Colorado to the Union. (Perhaps I should note that Grant was a notorious drunk, remembered not for being president, but for an uncomfortable Palm Sunday he spent with Robert E. Lee.) I cannot determine when the trophy was introduced to the rivalry. Some sources insist that every game between the team has been for the cup going back to 1893. If you believe that, then you probably think this is an authentic portrait of Benjamin Disraeli.

Above: The ornate Governor's Cup that Kentucky and Louisville play for, pic from CardinalSportsZone.com

Governor's Cup- Kentucky Wildcats vs. Louisville Cardinals- 9/2/2012
Since 1994, these two schools have exchanged their version of  Governor's Cup (for there are others) to signify football dominance in the Commonwealth of Kentucky. The trophy itself looks pretty and it seems to have the desired effect of incentivising a strong performance from both teams. In the last 12 years Kentucky has only one 4 times in their first game at an opponent's stadium, all of them were at Louisville. Similarly those were the only 4 home openers the Cardinals have lost in the last 14 years, but they have won two of the last three games played at Louisville. (All of this is starting to sound like I'm promoting a gambling tout's hotline, so I'll move on.) My main issue is that the Governor's Cup doesn't seem especially prized by other school. Both of these universities make basketball their number one athletic priority. When the Wildcats and the Cardinals met in the 2012 Final Four, it was said to "transcend imagination". I would guess that that sort of hyperbole will never be deployed to describe a game for the Governor's Cup. 

For Those Who Do Not Bowl
Each week I will use this space to highlight one trophy contested between teams from the less covered divisions and subdivisions of college football.

Above: The bronzed cleats of Myron Claxton, photo from OxyAthletics.com

 Myron Claxton's Shoes - Occidental Tigers vs. Whittier Poets- 11/3/2012
The hardware that appear farther up in this post have prestige and fame, but they cannot match the pure whimsy of a keepsake like Myron Claxton's Shoes. The story of this pair of bronzed sneakers dates back to 1939. Even then these two Southern California schools had a pretty good rivalry. After six straight Poet victories, the animosity had reached a level that members of the Occidental football team attempted to sabotage Whittier's All-American tackle by stealing his football cleats on the night before the game. Undeterred, Claxton took the field wearing his work boots. The Poets thumped the Tigers 36-0 and after the game Myron Claxton reclaimed his shoes from the Occidental sideline. Claxton would be selected in the next NFL draft, last overall pick a.k.a. Mr. Irrelevant, but still he was drafted. When the two schools met in 1946, a Whittier fraternity had bronzed the booties and placed them up to be claimed as booty by the winning team. The Tigers won that game and the boots have been handed back and forth ever since.

There is one more aspect of this game that interests me. In 1939, the man who would become the most famous Whittier alumnus, President Richard Milhous Nixon, was living in the area practicing law professionally. It is very possible that he attended the game to cheer on his Poets. However I somehow doubt this. If he had seen Claxton triumph over the Tigers' prank, surely he would have learned the dirty tricks do not pay.

Please return to this space each week during this college football season for more information and lore about college football's many trophies.  

The College Football Trophy Room: Introduction

Above:The Crystal Football awarded to the champion of the coaches' poll may be the most famous prize in college football, but it is far from the only trophy in the game.

So many things make college football special that, if I tried to write a list, carpal tunnel would set in before I could get half-way through. Yet somewhere near the top of my list -written well before pain crippled my pudgy, little hands- would be the unique wonder of trophy games. In no other sport I can name are teams awarded an hallowed artifact based on the outcome of an individual regular season game.

Trophies could be awarded for any number of reasons, to mark long standing rivalries, to signify respect between two schools, to reflect the pagentry surrounding a game, to boost the enthusiasm among the fans, or just because a bunch of drunken college kids thought it would be fun back in 1933. As varied as the reasons to have a trophy can be, the forms these trophies come in are even more diverse. On top of the many cups, bowls, and standard trophies, college football teams compete for buckets, skillets, rags, axes, jugs, shoes, golden hats and wooden turtles.

The raw number of prizes won and lost in a season will likely surprise/horrify the casual fan. So far my research has discovered more than 150 trophies still actively awarded to various game-winners.  Included in that number are six different Governor's Cups, five different Victory Bells, and one Governor's Victory Bell. If someone were so inclined, we could assemble a very impressive trophy case with all the baubles and tchotchkes at stake over the course of a season. In a sense that is what I intend to do over the coming weeks.

This entry launches my new blog series focusing on the wide array of trophy games to be played over this college football season. Each week I will explore different aspects of the games that decided who receive these prizes, the teams that will compete for them and the physical objects of reverence themselves. The goal will be to highlight a key trophy up for grabs during the coming weekend and take note of all the games being played for spoils in the FBS. (Completely tangential aside: FBS stands for "Football Bowl Subdivision"  to differentiate the high-profile portion of NCAA Division I schools that play in bowls from those that play in a championship playoff or FCS. Well now that the playoff proponents have won their much desired 4-team playoff for FBS starting in 2014, won't that make the current monikers obsolete. Maybe we'll go back to I-A and I-AA. Though I would like to hear some alternative suggestions.) In addition to the top-level rivalry games many of you already have heard of, I will feature some of the trophies that the less famous schools play for. Trust me there are some really interesting items up for grabs in Divisions II and III. So please check this space regularly during the college football season. I hope to get you all so excited for these trophy games that you start clearing some space on your mantle.

Ain't No Cure for the Summertime (Bite-Sized) Reviews

Once upon a time, I would use the powerful platform I have as a virtually unread blogger to shape the public discourse about the popular motion pictures of the day. My pronouncements on photoplays were brief but poignant insights. I eschewed lengthy recapitulations of plots and recommendations of which movies were worth seeing. Instead I offered punchy observations and analysis to help my readers spark conversations. I called these Bite-Sized Movie Reviews (though I've been inconsistent on using the hyphen). Then for a prolonged period I disappointed my audience by failing to deliver these movie morsels. Well, rejoice fair reader, because at long last I have a collection of thoughts on a few of this summer's blockbusters and some underexposed cinematic gems. Hopefully, you will learn a great deal from my musings and be inspired to share some witty thoughts of your own.

Marvel's: The Avengers-

• Let me start with the awkward title. While the group of superheroes known as the Avengers is a well-established brand (at least among U.S. comic book nerds), they aren't the only franchise marketed under the title "The Avengers". So Marvel probably wanted to distinguish a movie they hoped would succeed from an earlier film of the same title that bombed painfully. (When you click on that last link be sure to compare the film's gross to it's production budget.) In fact the earlier Avengers movie went over so poorly it almost pulled a triple-homicide on the careers of Ralph Fiennes, Uma Thurman and even Sean Connery.  Additionally, I suspect the leaders of Marvel's still nascent movie studio were concerned about audiences recognizing how they had interconnected multiple movies. To the average movie-goer there might be no clear connection between The Avengers and Thor or Iron Man or The Incredible Hulk except for the shared Marvel brand. So to maximize their potential audience, Marvel's marketeers didn't want anyone to misunderstand what was going on here. It worked too. As the first über-sequel -following up on multiple films that were only partly connected- The Avengers has earned more than any of the previous Marvel movies; putting aside the Iron Man movies it has grossed more than all of the lead-ins combined.
• I knew I had no reason to see the movie Battleship (Yes, this is still about The Avengers. Just hang on a second.) as soon as I learned that at no point during the movie does anyone say, "You sunk my battleship." That is the one vital line any script for that movie HAD to contain. The fact that the filmmakers didn't realize they had to include it -even if only ironically- was all I needed to know to not want to watch that movie. The fact that it also appeared to be the cinematic equivalent of a septic tank overflowing was just affirmation. I tell you this to help explain why I felt a little disappointed when a friend noted that no one says "Avengers assemble!" in The Avengers. I wouldn't have said I was a stickler for catchphrases before this summer, but apparently I am.
• On the topic of the film's commercial success, you may have heard a certain amount of cheering erupt from some of the geekier corners of Internet as The Avengers broke all kinds of box-office records. That was the sound of millions (or, more likely, thousands) of fans rejoicing that geek idol Joss Whedon finally had a profitable project he could point to as validation for all of his creative brilliance. His career began as an unheralded writer for sitcoms like Roseanne, while making uncredited contributions to screenplays for various hit movies. Life in Hollywood wasn't a bowl full of cherries though. On many films he found himself pushed out of the creative process and frustrated by the decisions of others. Once he became so infuriated with his supposed collaborators that he dented a bathroom stall venting his anger. Mr. Whedon first achieved a cult-like popularity when he adapted his creation Buffy the Vampire Slayer from a disappointing movie into a much beloved TV series. Since Buffy and its spin-off Angel became minor television successes, Joss launched multiple projects. Some of which were cancelled before their time in spite of critical acclaim. Nothing he's done has ever crossed over into mainstream success despite many people taking a strong rooting interest in his career. At long last as the writer and director of The Avengers, he has proven that his work can connect to a large audience. Hopefully this will clear his path to bigger and better things. For now though, Mr. Whedon can take a much deserved bow.
• Throughout Joss Whedon's career he has been known for a few trademarks in his work: witty writing, clever plot twist, a deft sense for sincere emotion, and frequently casting the same actors. After watching The Avengers with your typical star-studded Hollywood cast, I wondered what it might look like if you recast the movie with a cadre of actors more familiar to the Joss Whedon oeuvre. The following is a breakdown of who I would have liked to see in an alternate universe version of The Avengers.I invite you to look up any of the actor with which you are unfamiliar. I'll even provide the links. They are all delightfully talented, even in things not involving Joss Whedon.
  Role                            Movie Cast                           Whedon Cast
  Iron Man                    Robert Downey Jr.                Alan Tudyk
  Captain America     Chris Evans                              Nathan Fillion
  Thor                             Chris Hemsworth                   Adam Baldwin
  Hulk                              Mark Ruffalo                           Sean Maher
  Black Widow              Scarlett Johansson              Christian Hendricks
  Hawkeye                    Jeremy Renner                      David Boreanaz
  Loki                              Tom Hiddleston                Jonathan M. Woodward
  Phil Coulson              Clark Gregg                            Tahmoh Penikett
  Maria Hill                   Cobie Smulders                     Felicia Day
  Prof. Selvig                Stellan Skarsgård                  Olivia Williams
  Nick Fury                   Samuel L. Jackson               Chiwetel Ejiofor
  Pepper Potts             Gwyneth Paltrow                  Amy Acker
  Jarvis (voice)            Paul Bettany                        Anthony Stewart Head
  The Other                   Alexis Denisof                        Alexis Denisof 
  (OK, that last one didn't need to be changed)
  Council Chairman   Powers Boothe                       Harry Lennix
  *spoilers* Thanos   Damion Poitier                      Brian Thompson

The Cabin in the Woods-

• I've included this in my bite-sized reviews, mostly because I wanted to point out another movie Joss Whedon had a major role in making that didn't do to well at the box office. I don't understand how a horror movie that humorously deconstructed the genre couldn't earn at least as much money as Scream. As someone who hasn't enjoyed the Saw-ification of horror movies in recent years, I thought this film provided plenty of clever touches that horror fans and non-fans could enjoy. The fact that this film couldn't find a larger audience nicely exemplifies the snake-bitten nature of Joss Whedon's pre-Avengers career.
• Even without Whedon's involvement, I still would have been attracted to this movie if only for Bradley Whitford's presence. I can't quite explain it, but I find that man irresistibly charming in pretty much everything I see him in, especially when he's doing comedy. I like him so much, that part way through Kate & Leopold, I was actively rooting for Meg Ryan to abandon Hugh Jackman and go for Whitford's character instead.
• You may not find Cabin in the Woods at the cinemas anymore, but I think you might enjoy it even more on home video. The filmmakers seem to have made more of an effort to cram this movie with Easter eggs than any other movie I've seen. Off the top of my head I can think of four points in the movie when I wished I could have paused to take in all the little details that were captured in frame. That doesn't even count Anna Hutchison's final scene.

Moonrise Kingdom-

• Having watch and thoroughly enjoyed many of Wes Anderson's films, I think I may have noticed his most distinguishing trait as a filmmaker. He loves to use obfuscation, usually followed by an ironic revelation. We get a lot of that in this picture so it stood out enough to catch my attention. You have a shot of a scout that seems veritably Norman Rockwell until the camper turns his head to reveal a bandaged eye. At one point we are given a clear accounting of the simple supplies in a primitive campsite, only to have a large box of tinned food suddenly revealed. Anderson uses music and distance to prevent the audience from hearing certain pieces of dialogue. He writes dialogue that dances around the subject -in Moonrise Kingdom there is an important sublot involving Bruce Willis's character that is never explicitly stated but very clearly implied. Wes Anderson subtly challenges his audiences with this tactics. He asks them not just to watch and listen, but to consider what they cannot see or hear.
• Another persistent quirk in the films of Wes Anderson is his particularly mannered style of dialogue (one of many, along with panning through buildings like they were dollhouses, strangely retro art direction, and soundtracks that play like concept albums). Every character speaks in a idiosyncratic style where all of the emotions ring true even thought the actual words never sound like anything you'd hear in quotidian language. Somehow the affected cadences and precious witticisms seem to sound equally likely no matter which character says them. Anderson writes with the same voice regardless of age, sex, race, or class. With such a distinctive authorial voice every type of person is placed on a level field with no one presented as inferior or excluded. This creates a beautiful sort of equality between all of Anderson's characters where everyone is on equal terms. If writers want to avoid accusations of sexism, racism, or similar prejudices, I recommend using Wes Anderson as inspiration.
• This film presents the central characters as a pair of troubled and misunderstood preteens running away from home and struggling to understand the approach of adulthood. However if you are a cynical sort (Guilty!), you could also interpret this as a pair of developing psychopaths on the verge of breaking loose from all societal restraints. My knowledge on this subject is largely based on watching reruns of Criminal Minds, but as I understand it there are a few key warning signs for dangerous behavior and between the two leads we see all of them. You witness abuse/mistreatment of animals, fire starting, bed wetting, violent outbursts, and a complete inability to emotional relate to peers. I don't really think the kids are evil. I just worry you could watch this movie as a prequel to Bonnie and Clyde.

Prometheus-

• When you talk anyone who hasn't seen this movie they deserve to know first and foremost that Prometheus is much more of a horror story than a science-fiction tale. The central mystery of possible extraterrestrial interference in the early development of humanity gets sidetracked by prolonged sequences of monsters threatening people with gruesome deaths. I can even point to a couple of scenes where the logic of events (and possibly physics as well) get tossed aside to justify some additional action beats in the plot. It does succeed in frightening the audience to a disturbing degree, After my own father saw it he said he almost regretted having watched it he found it so disturbing.
• The promotional hype for this movie focused mostly on the director Ridley Scott. That's understandable since he was returning to the Alien franchise. However I felt most aware of  another creator's influence while watching the movie: the co-writer, Damon Lindelof. You may know him from his brilliant/confusing work on Lost (link leads to cussing). I couldn't help but noticed some important themes Prometheus shared in common with Lost. There are small things like folks troubled with daddy issues, or women struggling as their infertility suddenly leads to a life threatening pregnancy. Even the storytelling structure feels very similar to Lost.  We get puzzling glimpses into the underlying mythology of the universe and are left with numerous unanswered questions at the end of tale. I didn't mind that stuff when I watched Lost, so it doesn't bother me in Prometheus. Though I am well aware that there are loads of people who find that sort of thing pretty upsetting.

The Hunger Games-

• This was also a movie I watched.

Snow White and the Huntsman-

• One of the more interesting pieces of film criticism I have ever read was actually written by a sports writer. Bill Simmons once wrote a column about the movie Two for the Money in which he made clear that he enjoyed the film without ever crossing the line to endorsing it to his audience. My favorite part came when he tried to write a one sentence review that couldn't be used for blurbs in commercials and ended up writing, " Not only is "Two For The Money" surprisingly un-gawd-awful, I found myself feeling the opposite of mildly unentertained for a prolonged period of time that nearly coincided with the end of the movie."  Basically this parallels my feelings about Snow White. I had worried it would turn out to be a dud that spent loads of money instead of coming up with any good ideas. In the end though, I was surprised by how much I didn't dislike it. It may not have been brilliant, but it worked as a simple summertime entertainment. The script was pretty dull, though thankfully not completely formulaic and predictable. While I generally enjoyed the look and feel of the film a few scenes toward the end were weakened by an effort to squeeze in a few more special effects. I actually would recommend others to see it, if they can tolerate fantasy films. It just goes to show you that sometimes low expectations can be the best thing about a movie.
• I was intrigued with the prospect of this movie based on the strong visuals I saw in the advertisements.  Then I learned that the director Rupert Sanders had made a short film based on an excellent comic book, and my interest level went up several notches. When I watched the video online, (Heads-Up: It contains adult-type content.) I admired how well Mr. Sanders had captured the mood and visual style of the comic. That's when I knew that I would be seeing Snow White and the Huntsman at some point, if only on video a few years from now.. It delivered a lot of what I expected, gorgeous costumes, sets, and visual effects, and something I hadn't anticipated, straight-forward, unobtrusive directing. Rupert Sanders made his influence felt in his short film by making some eye-catching choices. In the feature he mostly stood back and let the film play out in a clean and simple manner. He didn't include a lot of attention grabbing shots or force in any flashy camerawork or editing for the purposes of showing off. What impressed me most about his directing style was that I almost never thought about it during the course of the film. Controlling your creative urges to deliver a clean and competent product marks a true professional, and I expect Mr. Sanders to do very well in the future. 

Those are all the words I feel like making you read this time. Though if you feel inspired to write any of your own, I would be glad to read them. Consider it my way of paying you back for my prolonged absence.

A Mathematical Proof 2500 Years Too Late

As a teacher I learned that one of the most important steps in educating someone is understanding how they think through a problem. To best understand how you take in and retain information, you must "unpack" your own thought process. You have to acknowledge every step your mind takes when it studies, analyzes, and solves a problem. It can be difficult to slowly and deliberately review each step of your thinking process like this, but you will be rewarded with improved problem solving skills. It's just like taking apart a machine to understand how it works so you can then make better use of it and take better care of it.

I recently went through this process myself when I got a particular mathematical ant in my pants. I am currently reading a novel that made a mention of the Pythagorean Theorem in passing. The character in the novel had such natural mathematical talents that the Theorem made immediate intuitive sense to her. Reflecting on this savant-like brilliance, I tested my own understanding of the Theorem. Almost everyone who has studied geometry remembers Pythagoras's most famous equation,  "A squared plus B squared equals C squared." If you were a good enough math student, you also remember that this equation describes a natural relationship between the three-sides of any triangle that has one corner at an angle of 90-degrees a.k.a. a right triangle. My problem was I couldn't remember how to prove the Pythagorean Theorem. This seems especially silly to me because Pythagoras originally demonstrated his proof about 2500 years ago.

In mathematics it is never enough to simply trust that an equation or rule works, you must be able to prove it. You can't just demonstrate it inductively either. To prove Pythagoras it would not be acceptable to show that 3^2 + 4^2 = 5^2 (feel free to pause for a second and check that arithmetic if you want) and a triangle with sides measuring 3, 4 and 5 units would have a right angle. Mathematicians don't take a rule that applies to a handful of examples and say, "I assume it works like that all the time."  An effective proof takes established rules and applies them to a generic example so as to create a universally applicable statement.

Lacking the ability to leave questions unanswered, I took my ignorance as an opportunity to test my mathematical thinking. I also decided to write down my process so that I could "unpack" the logical process necessary to prove something in math. Because I have blogged about education topics in the past, I though some segment of my readers might take an interest in unraveling the bundle of thoughts involved. By making my geometric contemplations explicitly clear and simple, I hope to help fellow educators find ways to help their students think through math problems.

An illustrative triangle

To prove the Pythagorean Theorem I needed to use deductive reasoning. So I began by writing down all the facts I could think of that related to triangles. From those points I could begin building my reasons to demonstrate the relationship between the sides of a right triangle.

I began by noting that for any triangle the angles of the corners must add up to exactly 180 degrees. This makes intuitive sense, because you can imagine a triangle as a path that takes three turns to point you in the opposite direction. As we all know, a reversal of direction is 180 degrees -or pi radians if you prefer.

Next I recalled the equation for calculating the area of a triangle, Area= 1/2*base*height. You can see how this works with a simple thought experiment. If you take any triangle and add a conjoined copy like a reflection across one of the sides, you have quadrilateral (i.e. a 4 sided shape) with an area equal to the triangle's base time's the triangle's height. Naturally the area of the original triangle is half the area of this new quadrilateral or 1/2*base*height.

The last fragment of knowledge I drew on was a little more advanced. I knew that there was a relationship between the size of an angle at the corner of a triangle the length of the side opposite to it. This is the basis for those trigonometric functions that probably traumatized most people in geometry class, sine, cosine, and tangent. This makes intuitive sense when dealing with a right triangle. The largest side, called the hypotenuse, is always opposite of the 90 degree angle (which must be, by definition, the largest angle in the triangle).

An example of a 45-45-90 triangle

This is useful because it establishes that in a right triangle with two equal angles of 45 degrees each, a 45-45-90 triangle, the two sides other than the hypotenuse must be equal because they are opposite equal angles.

The reason I focused on the example of the 45-45-90 triangle is because it has some special properties. In the same way we could imagine a quadrilateral made out of two identical triangles, we can create one square out of four identical 45-45-90 triangles. Just picture the hypotenuse as one side of the square with the four 90 degree angles joined in the middles.

One square which contains four 45-45-90 triangles

We can analyze this square to help prove the Pythagorean Theorem (in case you forgot during my babbling about triangles facts, that was the point of this exercise). First, we establish the total area of the square. Since all sides of the square are the length of the hypotenuse,or side C, we can easily calculate its area. The area of a square is the same as any quadrilateral the length multiplied by the height. In a square those lengths are both the same as the length of one of the sides. So area = side * side = side^2. In this square the length of the side is called C so the area is C^2.

We also know that the total area of the square is the same as the combined area of the the four triangles. As discussed above the area of a triangle is given by the equation area = 1/2*base*height. You multiply the area of one of those triangles by 4 and you get this:

4 * area = 4 * (1/2*base*height) = 2*base*height = total area of square

Since the base and the height, which we can call side A and side B, are both the same length we can simplify the above equation for the square's area.

2*base*height = 2*side*side = 2 (side^2) = side^2 + side^2

We can substitute side A or side B in for either side length in this equation. That allows us to rewrite the area of the square as Area = A^2 + B^2 = C^2. This proves the Pythagorean Theorem for all 45-45-90 triangles. 

I started with proving the Theorem for 45-45-90 triangles, because I knew they had special properties that made them easier to work with. Unfortunately you can't create a simple square out of every right triangle. Still, knowing that I had worked the proof for one class of triangles, gave me an insight for working a broader proof. In order to prove Pythagoras correct for all triangles, I had to find a more sophisticated method that I could apply to any type of right triangle. I was able to work from the foundation of my earlier exercise by searching for ways to create squares using the sides of triangles.

My breakthrough came when I realized that any right triangle can be used to define a square area. (This was important because, as I would learn later, earlier generations had used this as the basis for other proofs of Pythagoras.) You can form a square by arranging four identical copies of so that their right angles form the corners of the square.

The square defined by the combines sides of  four copies of a triangle

In order to keep the sides equal length we'll combine all the triangle legs of length A against all the legs of length B. This gives us a square where the length of each side is A+B. Since we get the the area of a square by multiplying the length of a side by itself, we can calculate the are of this square in the following way:

Area = (A+B) * (A+B) = A^2 + 2AB + B^2

When you arrange the triangles in this manner, the hypotenuse of each triangle forms the side of another smaller square with the square discussed above. Since all the sides of this square have the length of the hypotenuse, which we call C, you can define the area of this square as C^2. The area of the square with sides of A+B can be redefined as the area of the hypotenuse square plus the area of the four triangles. Each of the triangles has an area of 1/2*A*B.

Area = C^2 + 4(1/2*A*B) = C^2 + 2AB

We know from our earlier definition of the larger square's area that the area is equal to A^2 + 2AB + B^2. Therefore

Area = A^2 + 2AB + B^2 = C^2 + 2AB

Because the two quantities are already equal, we can perform any mathematical operation to both sides and they will still be equal. In this case we can subtract the quantity 2AB from both sides because in exists in both expression. This leaves us with A^2 + B^2 = C^2. This proves the Pythagorean Theorem for all right triangles.

Just for clarity, I do not recommend any math teacher tries to explain the Pythagorean Theorem using my meandering thought process. Instead I hope teachers of all kinds appreciate that though my method may not seem perfect it achieved the desired result. The purpose of unpacking is often to find the twists and kinks in a person's reasoning, but it can also demonstrate that differing methods of thinking can be acceptable. Students need to know that there is no one right way to go about thinking. Every teacher should encourage students to unpack their thinking, so they can see that -however they go about reasoning- they can always find ways to sharpen their thinking. You can always improver your problem solving  even if it means solving a problem 2500 years too late.

Arbirtrary Bowl Predictions: Alumni Face-Off- BCS Bowls

The first year Clemson graduated students was also the first year they played a football game. Coincidence?

The biggest bowl games of the college football calendar deserve the best predictions I can muster. (Too bad I'm still pretty hung over from New Year's Eve.) So I have arbitrarily chosen to pick the games based on a comparison of alumni I arbitrarily select from all the schools involved and then analyze them based on my completely subjective opinions. After all of this I probably haven't offered any useful gambling advice, but hopefully I spurred some interesting conversations.

Rose Bowl- 5pm 1/2/2012
Rose Bowl, Pasadena CA
Wisconsin Badgers vs. Oregon Ducks (-6.5)
The Alumni:

John Muir

VS.

Phil Knight

Very few match-ups have featured alumni who would probably hate each other. John Muir was an early vocal advocate for environmental issues. He was a naturalist who founded the Sierra Club and helped to preserve Yosemite and other American National Parks. The state of California chose to honor John Muir when they printed their state's commemorative quarter. If here were around today he would likely spend his time challenging major companies for their practices that harm the environment. One company the Sierra Club has clashed with is Nike, founded by Phil Knight. Knight turned a small side-business selling shoes into the world's leading producer of sporting goods and apparel. He has been a tremendous booster of the University of Oregon, getting them uniforms, equipment, and even a new basketball arena. Nike has gained a reputation for controversial business practices. Knight would doubtlessly find activists like Muir a hindrance to his business.

The Prediction: These alumni indicate very different game plans by the teams. Wisconsin will try to stay "grounded" and run the ball hoping to preserve a small lead. Meanwhile the sleek and modern style of Oregon will show in their aggressive attacking style. Over time the Ducks will find an opening and gain a lead, and the Badgers won't be able to catch up
Oregon- 48 Wisconsin- 28. 

Fiesta Bowl- 8:30pm 1/2/2012
University of Phoenix Stadium, Glendale AZ
Stanford Cardinal vs. Oklahoma State Cowboys (-3.5)
The Alumni:

Herbert Hoover

VS.

T. Boone Pickens

You may not appreciate how tremendously successful both of these alumni are. Despite the common perception of Hoover as a terrible president, he actually had a fabulous career outside of his time in the Oval Office. He was a successful businessman. He organized humanitarian efforts surrounding World War I. As the U.S. Secretary of Commerce, he spearheaded a number of efforts to help modernize America. If the entire global economy didn't collapse during his time in office, we might remember Herbert Hoover in kinder terms. Similarly T. Boone Pickens has done more that just succeed at the oil business. He has become a powerful political player. He supported the Swift Boat Veterans for Truth group that attacked John Kerry's 2004 presidential campaign. Lately he has been pushing for a radical shift in American energy policy toward petroleum alternatives.

The Prediction: I foresee a game that may appear to be disappointingly low scoring, but actually is very entertaining for football purists. The teams will both play a smash-mouth style and execute sharply. The defenses will look good keep the game moving at a quick clip. Overall the Cardinal will have a more flexible attack and scratch out a few more points than the Cowboys.
Stanford -19 Oklahoma State- 13 

Sugar Bowl- 8:30pm 1/3/2012
Superdome, New Orleans LA

Michigan Wolverines (-1.5) vs. Virginia Tech Hokies
The Alumni:

President Gerald Ford

VS.

Homer Hickam

Usually when the other school can list a U.S. President as an alumnus the other school would have a hard time matching-up. In the case of Gerald Ford though, he may be a little vulnerable. After all he was never elected on a presidential ticket and he only finished out a term after Nixon's resignation. I also really admire Homer Hickam who has the inspiring story of rising from a small coal mining town to become a NASA scientist. The reason I give the edge to Ford is because he combines a notable life after graduating with a successful career as a football player when he was at Michigan.

The Prediction: You may not enjoy watching this game. Michigan will alternate between looking sharp and committing costly errors. The Hokies won't be able to capitalize on the numerous turnovers and penalties, and will only be able to keep the game close without ever really threatening.
Michigan- 20 Virginia Tech-16


Okay, in previous posts I have tried to disguise fake bowl games as the genuine article. Since this post only focuses on the BCS bowls, I knew it would be impossible to convince you some new high profile bowl had been created. So instead I have proposed an alternative game. Instead of controversially picking Michigan and Virginia Tech for the Sugar Bowl, they could have picked the two highest ranked teams eligible for BCS bowls, Boise State and Kansas State.
Aspartame Bowl- 8:30pm 1/3/2012
Superdome, New Orleans LA
Boise State Broncos (-6.5) vs. Kansas State Wildcats
The Alumni:

Frances Rogers one of the protagonists of the novel Little Lost River, attends Boise State

VS.

The hero of the film The Secret of  My Success, played by Michael J. Fox, is fresh out of Kansas State

In honor of this clearly fictional bowl, I have selected two clearly fictional characters. Now I have neither read the book or watched the movie in which these characters appear, so I cannot give much of a description. In Little Lost River the character Frances Rogers attempts to bond with another young woman after a tragedy while she transitions from high school to college at Boise State. Michael J. Fox played Brantley Foster a recent college graduate who travels from Manhattan, Kansas to Manhattan, New York. He somehow becomes a success despite a comedic plot trying to get in the way. I have to assume the KSU grad had the more impressive fictional accomplishment.

The Prediction: Boise State will start slow and stay that way. Kansas State will have an awful start, but they'll use a trick play to gain momentum. After getting their spirits lifted by a surprise score, they will coast to a win.

Kansas State-17 Boise State-12

Orange Bowl- 8:30pm 1/4/2012
Sun Life Stadium, Miami FL
West Virginia Mountaineers vs. Clemson Tigers (-3.5)
The Alumni:

Jerry West

VS.

Jonathan Hickman at a comic book convention

Jerry West was a legend on the basketball court. He is even rumored to serve as the model for the NBA logo. After his playing days he became a very successful NBA general manager. He headed up multiple championship teams and won the NBA Executive of the Year award twice. That's all pretty impressive for a kid from the banks of Cabin Creek in West Virginia. Unfortunately for Clemson the only alumnus of theirs I likes is Jonathan Hickman. He has made hit independent comic books and written for the major superhero titles. I even had the pleasure of speaking to him once. However I don't think anyone is turning his silhouette into a logo anytime soon. 

The Prediction: In a total route the Mountaineers dominate from beginning to end of this game. I would watch something else when this game is on.
West Virginia- 42 Clemson- 13

BCS Championship Game- 8:30pm 1/9/2012
Superdome, New Orleans LA
Alabama Crimson Tide vs. Louisiana State Tigers (-1)
The Alumni:

Bear Bryant

VS.

James Carville

I would have loved it if the championship game featured the most distinguished alumni, but since Harvard and Yale don't play top level football that's unlikely. Instead we have two people known for their incomprehensible accents and what they have on the top of their heads (for Bryant the famous houndstooth hat, for Carville his shiny bald dome). Paul "Bear" Bryant  is THE face of Alabama football, as a former player he came back to Tuscaloosa to coach the team. His run as the leader of the Crimson Tide remains the stuff of legend. Carville was one of the key players in Bill Clinton's political team. Since helping win Clinton the 1992 presidential election, he has become a wildly entertaining TV personality. If you need someone to come on camera and argue the liberal position, or just say something outrageous, then Carville is your man.

The Prediction: LSU will try to pull off some crazy trick plays, and will fight all the way through the game, but Alabama will demonstrate a superior execution of football basics. It will be a close game and hotly contests from start to finish, but the Crimson Tide will never be at serious risk of losing. And I don't care because I think they should not have played this game at all. 

I hope everyone enjoys the bowl season, and I hope to bring you more bowl predictions the next year I have a good idea and time to write.

2011 Arbirtrary Bowl Predictions: Alumni Face-Off Part 4

The 1905 Pittsburgh football team (note: at the time of this photograph the University of Pittsburgh was named the Western University of Pennsylvania and football was still referred to as "hand-soccer")

A new year has begun (which for some means they resolved to stop gambling) and the bowl season will conclude soon (which means we have a great excuse to break that resolution already). I invite you to base your first wagers on 2012 on my arbitrary bowl selection method. As explained in earlier posts in this series, I have analyzed the bowls by comparing representative alumni of the schools involved in each game. I enjoy giving absurd gambling tips so much, that this year I have even created fictional bowls. While you read this post, try to guess which bowl is actually a fake.

TicketCity Bowl- 12pm 1/2/2012
Cotton Bowl, Dallas TX
Houston Cougars (-9) vs. Penn State Nittany Lions
The Alumni:

Matt Mullenweg

 VS.

Herman Fisher

Since pretty much everything I do in life can be described as "derivative", I have to tip my cap to the innovators in life, such as these to alumni. Matt Mullenweg may not have had an award-winning movie made about his life, but he founded websites that reach a billion people every month. One of his creations, WordPress, is one of the most popular blogging platforms on the web. Herman Fisher is the "Fisher" in "Fisher-Price" toys, the toy company he founded during the Great Depression. This man created the term "preschool toys" and landed the first deal to produce licensed Disney toys. Odds our your childhood was shaped by the influence of Herman Fisher. In the end though I think I will favor Mullenweg, because we bloggers have to stick together

The Prediction: You can expect a real contrast of styles in this game (Do I use that phrase to much?). Penn State will play fundamental, "ground-and-pound" football to try to limit the wide-open Cougar spread attack. The Nittany Lions want to keep the Cougar's offense off the field and make it a physical contest. I foresee Houston making the most of every possession though and putting up enough points to win handily.
Houston- 35 Penn State-20

Gator Bowl- 1pm 1/2/2012
Everbank Field, Jacksonville FL
Ohio State Buckeyes vs. Florida Gators (-1.5)
The Alumni:

Jesse Owens

VS.

Erin Andrews

Major public universities provide large pools of alumni to select from, so I can usually find something interesting. In this case, I found two people who were national sensations 70 years apart. The Buckeyes produced  track and field legend, Jesse Owens, who won four gold medals at the 1936 Summer Olympics in Berlin. The dominance of an African-American proved the falsehood of Hitler's claims of Aryan superiority. Former member of the University of Florida dance team, Erin Andrews reaffirms the superiority of pretty talented people. She has become one of the most popular personalities on ESPN and is such a hit online her nickname is "Erin Pageviews", because any pictures of her draw lots of hits (or at least I'm hoping that's the case). As excited as Erin Andres makes the masses, I think Jesse Owens has to be favored for performing one of the greatest athletic feats in history. At the 1935 Big Ten track meet he claimed 4 world records in 45 minutes.I'll give you a second to pick your jaws off the floor.

The Prediction: This game will be fast paced and exciting all the way through. Both alumni indicate football teams capable of scoring lots of points in a hurry. The decisive moment will come in the middle of the game when Ohio State will score multiple times in a few minutes of gametime, which will give them an insurmountable lead.
Ohio State- 45 Florida- 34

Outback Bowl- 1pm 1/2/2012
Raymond James Stadium, Tampa FL
Michigan State Spartans vs. Georgia Bulldogs (-2)
The Alumni:

Magic Johnson No. 32 (photo by S. Lipofsky)

VS.

Herschel Walker on a Sports Illustrated cover

We have some superstar athletes to compare in this match-up. Erving "Magic" Johnson starred in the most watched college basketball game of all time. Then he authored a Hall of Fame career as a professional basketball player, winning multiple championships. Then he brought new levels of attention to the HIV crisis, as the most famous HIV-positive person. Then he became a successful businessman generating hundreds of millions of dollars worth of net worth. Now he has become a popular basketball analyst on TV. Herschel Walker may be considered to be the greatest college football player ever, but that is a lot to overcome.

The Prediction: The Bulldogs will run the ball well, and that will be about all they have work for them. Otherwise the Spartans will dominate the game in all three phases. Michigan State will score just about every way they can (e.g. returning kickoffs and interceptions for touchdowns) to cruise to an easy victory.
Michigan State- 48 Georgia- 16

Capital One Bowl- 1pm 1/2/2012
Citrus Bowl, Orlando FL
Nebraska Cornhuskers (-1) vs. South Carolina Gamecocks
The Alumni:

Heeeeeeeeeeeeeeeere's Johnny!

VS.

Darius "NOT Hootie" Rucker

As you may have noticed in my earlier posts, when entertainers meet I predict entertaining games. These alumni are especially entertaining. Johnny Carson hosted the Tonight Show for decades. Because millions dozed off watching his show year after year, he became the face of the late night television for multiple generations of Americans. Darius Rucker first gained fame as the lead singer for quintessential 1990's band Hootie and the Blowfish. They had a runaway hit album, then fell into obscurity. In recent years Rucker has risen to fame and fortune again as a solo artist performing, I kind you not, country western music.

The Prediction: The omens tell me that South Carolina will open strong take a big lead early. The Cornhuskers will just keep plugging away, to eventually take the lead. The Game Cocks will launch a furious comeback attempt in the closing minutes, but will ultimately fall just short.
Nebraska- 29 South Carolina- 28


North American Bowl- 8pm 1/5/2012
Rogers Centre, Toronto ON
Miami University RedHawks vs. Navy Midshipmen (-9)
The Alumni:

President Benjamin Harrison

VS.

President Jimmy Carter

Naturally the only bowl game played outside of the United States should involve two schools that produced Presidents of the United States. Neither of these men may be remembered as particularly great presidents, but I think you have to pick a POTUS over other alumni, especially since there aren't man times when two teams to produce presidents meet in bowl games. (Especially since Whittier College and Eureka College stink at football.) I think Navy has a big advantage in this game after comparing these two Commanders-in-Chief. President Harrison is the only president to lose a presidential election the someone who was voted out of the White House. President Carter has spent his time since leaving office as a leaded for humanitarian causes eventually earning a Nobel Peace Prize for his work. I think that might make him the greatest ex-president ever, with the possible exception of the dude who came back to beat Harrison.

The Prediction: The RedHawks may claim an early lead, but look for Navy to get stronger as the game goes on. The Midshipmen will look impressive after a slow start, and the RedHawks will deliver a thoroughly forgettable performance.
Navy- 42 Miami U.- 13

Cotton Bowl- 8pm 1/6/2012
Cowboys Stadium, Arlington TX
Kansas State Wildcats vs. Arkansas Razorbacks (-8.5)
The Alumni:

Taylor Mali

VS.

Pat Summerall  pictured on the cover of his autobiography

Both of these representative alumni have earned their livings with their voices. Mali has become possibly the most famous slam poet in the world. He uses his performances to try to inspire others to become teachers. So he will represent the school where he first taught. For millions of Americans, when they imagine a play-by-play announcer calling a football game, the voice they hear in their head belongs to Pat Summerall. he spent years covering NFL games and had such a great voice it has been used to narrate everything from golf video games to Looney Tunes cartoons.

The Prediction: Both teams will play with a lot of passion. Kansas State will lean on their strength of running the ball. Arkansas will prove more versatile and will keep KSU off balance all game. The Razorbacks will wear out the Wildcats as the game goes on, giving them a comfortable lead to end the game.
Arkansas 30- Kansas State- 21

BBVA Compass Bowl- 1pm 1/7/2012
Legion Field, Birmingham AL
Southern Methodist Mustangs vs. Pittsburgh Panthers (-7)
The Alumni:

Lamar Hunt (photo from Bat for The Cure)

VS.

Gene Kelly smiling as his own name hover in front of him

You have to salute the audacity of Lamar Hunt who was a wealthy oilman that loved football. Since the NFL wouldn't  let him join, he started the American Football League. He eventually forced the two teams to merge. His team still plays on as the Kansas City Chiefs. Gene Kelly had a remarkable career as a dancer and movie star. His film Singin' in the Rain, is generally considered one of the best movies ever made. Kelly was so iconic that when he died ABC didn't do the standard memorial. Instead they acknowledged his passing by playing his famous "Singin' in the Rain" sequence, an unprecedented tribute. I would love it if when I died my entire life could be perfectly summed up with a few minutes of film that I created.

The Prediction: I predict a bit of an ugly game at first. Both teams will need some time to get into the flow of the game. Once they do though it will be a fun match-up. The Mustangs will play aggressively and try for big gains every chance they get. The Panthers will execute flawlessly and use graceful play to gain leverage. Pitt wins the game with a well played 4th quarter to put SMU away.
Pitt- 30 SMU- 23 

GoDaddy.Com Bowl- 9pm 1/8/2012
Ladd-Peebles Stadium. Mobile AL
Arkansas State Red Wolves (-1) vs. Norther Illinois Huskies
The Alumni:

Arkansas Governor Mike Beebe

VS.

Markos "Kos" Moulitsas

Political match-ups can be tricky. I worry that it will look like I am choosing the victor based on my politics. I try to make all these predictions based not personal preference, but on a fair assessment of the relative merits of the respective alumni. In this case I feel like winning the Arkansas gubernatorial election isn't as much of an accomplishment when compared to founding one of the most popular political websites, Daily Kos. I just know this post will draw Bill O'Reilly's ire, for supporting someone he considers to be a "left-wing extremist".

The Prediction: This game will be more of physical struggle. It won't be much fun to watch, as both teams will seem more intent on injuring the other team than scoring points. I expect NIU will carry a narrow lead throughout the game to win in "not as close as the score" fashion.
NIU-23 Arkansas State-20


The games are starting soon enough, so I'll let you stop reading now. I will have my prediction for the BCS Bowls in the next installment.