Highlights from Los Alamos Speech and Debate Tournament, 2013

At 6:00 am Friday, November 1, participants in “congress” loaded the bus for Los Alamos with Ms Ontiveros. Their heads were surely swimming with Roberts Rules of Order and “legislation” that they and their competitors had written.   I left with the 12:30 group, which really left at 12:35 because some of our debaters refused to miss their 5^th period class, (“I didn’t want to miss any of Mr Kintinar’s class,” says Jessica Berry.)  I walked up and down the isle of the bus and saw Jaimie Lin reading Economist magazines to prepare herself for her International Expository Speaking event (see previous result email), Coach Sheridan Johnson prepping speech competitors in their events, Jessica Bregman practicing her memorization, and a variety of other rather heady activities.  

We arrived at the hotel 30 minutes before the first events, debaters and speakers piled out the bus to swiftly get themselves all gussied up for their events. Girls pull on stockings and pumps, boys tie ties.   We arrived at Los Alamos High school with about 2 minutes to spare before the first events.  Competitors ran swiftly between events; Georgia Purcell gathered burritos for dinner that our teammates ate on the run.  I could smell the sweet fragrance of adrenaline until we all shuffled into our hotel rooms at 11 pm. 

By 7:00 am all 33 speakers and debaters and the coaches were back at the school and the smell of adrenaline was laced with coffee.  Samsara Durvasula was excited (yes, excited) to complete some trig proofs with me at 7:30 am; English students were watching a required movie (yes, at 7:30 am) and discussing the ideas in the movie.  Copies of the AP Bio text were opened as our debaters and speakers read between their rounds.

Lincoln-Douglas Debate. Jess Berry. Topic: Resolved: In the United States criminal justice system, truth-seeking ought to take precedence over attorney-client privilege. With the maturity and poise of Elizabeth Warren and the vocabulary of a seasoned speaker, Jess stands before the judge and begins her case:  “Rape culture is perpetuated by our system of attorney-client privilege; insights from the German system of justice, founded after an era of genocide, could help us develop a system that allows truth seeking…” Well-read, articulate, brilliant, creative, and able to moderate her speeches to fit the skills of the judges, Jess wins the first sets of rounds handily, even earning a perfect speaking score from the experienced Los Alamos coach.

 Suddenly, it was evening and the results of the two-day tournament were being announced. The highlight for everyone from AA was when the Novice Policy Debate results were being announced.  Eighth Graders Harrison Bay and Tari Muneri were standing poised facing the large audience as one of the top 6 teams. When their names were called last as victors of the entire tournament in Novice Policy Debate, the house came down with cheers and enthusiastic noise.  This was the first time Harrison and Tari had debated together; this was only their second tournament. They practiced their cases together, but had never (not even in practice) completed a full round together.  Diminutive in stature but obviously powerful in character and skills, they debated in a challenging arena: Policy.  Topic:    Resolved: The United States federal government should substantially increase its economic engagement toward Cuba, Mexico or Venezuela. Harrison downplays his success as if it’s all child’s play. When I asked how it went, he said, “We refuted their arguments; they dropped ours.”  No nervous energy here for a young man who has played the piano twice in Carnegie Hall; only beautiful shy smiles from Tari as she enjoys but still minimizes their success.  With a shrug, I hear, “I guess we did think well on our feet.  That was fine.”

Particular Kudos should be extended to the coach of the Policy Debaters.  Jeremy Pena comes to AA after his job in a law office and works with students on debate skills and the cases they argue.  The success of so many debaters is directly attributable to his good work with the students.

Other students who did well include:

Ria Mazumdar – FIRST in Domestic Extemporaneous speaking (30 mins to prepare a memorized 10 min speech on Domestic political or economic issues)

Nobel Barakat – SECOND in International Extemporaneous speaking (same as Domestic Extemporaneous speaking, except, of course, with international themes)

Sally Midani and Jess Bregman – THIRD in Duo Impromptu (An event for two people where the topic is chosen when they walk in the room and together they have to prepare a presentation)

Ria Mazumdar and John Chappell – SECOND in Varsity Policy Debate (same as what Harrison and Tari won but in the “varsity” category) Note that I wrote last time about John winning the novice category and being bumped up to Varisity because of his improvement)

Ariel Hurowitz and Harley Hanes – THIRD in Varsity Policy Debate

Sally Midani and Jaimie Lin – FIRST in Duo (A dramatic event where they choose, edit, prepare and perform a script)

Emily Louth – THIRD in OI (Oratorical Interpretation)

Margaret Downs – SIXTH in Original Oratory (You may remember her in the last email; she spoke about the value of good teachers)

Grace Kienzle – FIFTH in Original Oratory

GA2: Beauty and Geometry

I was just reading about the mathematician Tom Zhang and his fascination with "twin primes."

Please read this interview with this brilliant mathematician and consider at least one of the many things he's saying.  Choose something about his views of mathematics and write about it.

To get your creative juices flowing, a couple thoughts I had about the interview include (but are not restricted to):

1. The idea that mathematicians are born, not made.

2.  He views math as beautiful and interesting not at all for the application. He loves math for itself and for the way mathematics helps him use his mind.

3. I remembered something I read, written by Harold Jacobs in his Geometry text book from 1974:

Pythagoras was a Greek geometer who lived about 2500 years ago.  He wondered whether he could teach geometry even to a reluctant student.  After finding such a student, Pythagoras agreed to pay him an obel for each theorem he learned.  Because the student was very poor,  he worked diligently.  After a time, however, the student realized that he had become more interested in geometry than in the money he was accumulating.  In fact, he became so intrigued with his studies that he begged Pythagoras to go faster, now offering to pay him back an obel for each new theorem.  Eventually, Pythagoras got all of his money back. 

Now ok, a bunch of you admitted that you do some math in secret or in ways and times that you didn't think you were actually doing math. A bunch of you claimed that over use of technology contributes to math illiteracy.  Will any of you to admit that there's something in math --anywhere -- that you've found lovely, beautiful, cool, interesting, intriguing, puzzling, worth thinking about, or simply fun?  Oh, do share!

TPC: Who Uses Trig in His or Her Job and How is it Used?

Surveyors. That's the quick answer. Seems obvious and web searches will yield a plethora of sites that show trigonometry in surveying, but those surveyors have some deeper equations embedded into their programs.  Mollweide's Formula is one of them.  If you look at this equation, how many angles and how many sides of a given triangle are included in the formula?  Why, from a number theory standpoint, would this be a good thing for surveyors -- what would they use it for?  AND .....do you really think that the typical joe or jane surveyor would know this formula or even know of the existence of this formula?

Doctors.  Particularly, radiologists use trig as they aim gamma rays into the bodies of their patients to eliminate tumors without traditional scalpels. How do you think trig is used in this area? Orthopedists use angles in their work, just check out the abstract to this article:  http://www.ncbi.nlm.nih.gov/pubmed/7610093 or do a search -- there's lots available. Some images are not for those with a weak stomach.

Sailors. Just look for the triangles.                      

Rock Climbers and outdoor enthusiasts. Tyrolean Traverses  (Can you find the triangles, angles to measure....?)

Astronomers....

You get the idea.  In high school college-prep mathematics, trigonometry is often the first place students see direct applications of math in a variety of concrete areas.  For your blog, find an application,  a single application so you can develop it well, anything, and explain how trigonometry or the study of triangles applies to the field. Go ahead, ask parents, your friends' parents, anyone.  Do they use trigonometry? Where?  How?  You might find lots of people who say, "Nope, never used it."  Your mission is to find an application in the professional world.

Probability in the Pool: August 19, 2013

When my mom had a catastrophic stroke, I returned to my home town and found a pool in which to swim.  I swam mostly alone in a pool that was 50 meters by 25 meters.  Sometimes the lane lines were set to allow swimmers to swim "short course" (25 meters) or "long course" (50 meters).

On one of the short course days, I was alone in the pool.  There were 16 empty lanes.  I chose lane 8, one of the middle lanes.  I swam down-and-back (50 meters) in about 45 seconds.  This became a deliciously long swim as I moved back and forth alone in this pool with my own personal lifeguard.  Then, suddenly, I was jerked out of my fraction-calculating delerium (refer to previous post about Fractions in the Fast Lane) when waves overtook me.  A man dropped himself and his large belly covered in fur into the lane next to mine at precisely the moment I was at his end of the pool.

Ah, I thought.  A probability problem.   What is the probability that he would (a) choose the lane next to mine and at the same time (b) choose to enter the water during the roughly 7 seconds that I am vulnerable to the tsunami he created at the near end of the pool.  And is this probability small enough that I should think this individual inconsiderate?

On one of the long course days, I was again alone in the pool, now well spoiled and feeling like the Queen of Sheba in her own blue-glass lake (with lane-lines and a black line at the bottom.)  There were 9 lanes. I chose the middle lane.  I would swim 50 meters to the far end and 50 meters back, giving me new distances and fractions to consider.  I swam the same rate as in the short course setting in the pool.  Again, as I swam a deliciously long swim with new numbers flowing along side of me, another man, a more narrow man, entered the pool.  Now then, many of us in this world like to be individuals; we value our ability to make choices and to be unique.  This man decided to swim a uniquely different way in this pool.  He wanted to swim 25 meters, not 50 meters as the pool was set.  So he did, weaving his way across the pool, below the lane lines and intersecting my path perpendicularly.  My interest became piqued.  As I swam, I watched the red clocks surrounding the pool and observed that he swam breast-stroke quite regularly, finishing 50 meters (down and back, under the lane-lines) in about 100 seconds.

Ah, I thought. Another math problem. If we both start at the same place (let's say a corner of the pool, just to make this conceptually more straight-forward) and swim in paths perpendicular to each other, when (if at all) will we collide?  If we both leave one end of the pool at the same time and swim at our own constant paces, when (if at all) will we collide?  If a moment during our infinite-length swim is chosen randomly, what is the probability that we will be in a collision at that moment?  Consider that it would be about 7 seconds for me to be in his way; he'd be in my way for 1/9th of the way across the 25 meter pool.

TPC: Waves in the Pool

I swim at a constant rate.  Well, close enough; assume I swim at a constant rate, then we'll adjust that later in this blog.  That rate is roughly two meters for every second.  Well, ok, that's a little quick for this ol' lady, but those numbers work for us. So pretend.

Let's start by thinking of what a graph would look like as I cruise at my theoretical constant pace of two meters per second back and forth in a pool that is 25 meters long.  Let the x axis (independent variable) be time, measured in seconds, and let the y axis represent meters away from the wall, or side, of the pool.  Let's start our stopwatch at the exact time when I leave the wall and head to the other side of the pool.

How does the graph appear if I adjust my pace to 1 meter per second?  How about to 3 meters per second?  1/2 meter per second?

These kind of "waves" are not quite a sine wave. Wikipedia categorizes the waves as triangular:

http://en.wikipedia.org/wiki/Sawtooth_wave.

But there's more. Lots more.

How would the graph be different if I swam my 2 meters per second pace in a pool that was 50 meters long?

How would I need to swim differently to make the graph look like the other waves that the wiki pictures on the bottom right?  Which ones are not possible?  Spend some time with, of course, the sine wave and describe how I'd need to swim so that my distance from the wall would be a lovely, smooth sine wave.

So you've already seen that I do some interesting math while I swim. I can solve all the world's problems when I swim, you know. Now what happens if I'm swimming in the pool that's 50 meters by 25 meters.  I swim the long way at a constant 2 meters per second and another swimmer decides to swim the short way, perpendicular to my path and swimming a constant 1/2 meter per second. (No kidding, someone actually decided to do this last summer.)  I swim in lane one as does he (well, we don't but pretend we do) so we start at the same time and in the same corner. Because we are all thinking perfectly and precisely mathematically, we imagine triangle waves, but let's say we are so far advanced that both the other swimmer and I slow down and speed up appropriately so that the graphs of our distances from the wall with respect to time form perfect sine curves.  You've already worked out  how we adjust our speeds to make perfect sine curves, of course, because the previous paragraph asked you to do this.

So the bigger question is, assuming we can occupy the same spot simultaneously or that I can duck directly below the surface while maintaining my lovely sine curve pacing, how often do our paths intersect?

For your blog, either show graphs like I've described or take my idea a little further, maybe by answering the questions I pose, OR find your own application of a sine curve.  Where do YOU see it in the real world?

9%.

Fun to bike down but a workout to bike up, a 9% grade earns a failing grade in my gradebook. 

Outside of Otis, Massachusetts is a road with a very steep hill.  Put in neutral, our standard transmission car just cruised down the hill. On the way up, first gear was the way to go, so to speak. The rhomboid sign reported a 9% grade (“Test your brakes,” it warned). A biker was huffing her way up the slope while a second simply sailed down the hill.  What’s the 9% mean?  If 60% is passing and 90% is an “A,” what’s 9%? Doesn't seem like much; why the big deal on that hill outside Otis?  Folks seem to always aim for 100%, but that would be suicidal in an automobile or bicycle and certainly not preferable.  We, as humans, do our best to categorize (think: Kingdom, Phylum, Class, Order, Genus, Species or better yet square, rhombus, rectangle, parallelogram, trapezoid, quadrilateral); it seems we have categorized slopes (or grades) of hills as well. 

Wales has a road with a 25% slope; I-70 into Denver from the west has a cool 6% grade.  A handicap ramp has to be an inch vertically for every foot horizontally.  Are these ideas related? 

Your mission is to understand what these numbers mean and how engineers have come to categorize the grade of a road, ramp, or slope.  Nice word there, by the way, “Slope.” 

http://en.wikipedia.org/wiki/Grade_(slope). 

Yep, good ol’ Wikipedia actually has a description that works for us.  It may seem a little dense and might take some slower reading than, say, Ted Geisel’s stuff,  but it’s got all the ideas you need.  In the wiki, there are triangles, a protractor shape, a trigonometric function, and some other very familiar words.  Put the pieces together in your blog and you’re set for the week’s blog assignment. (Be sure you take out the irrelevant ideas for "grade" in my post -- this is meant to have nothing to do with the grade you get in class. That's a joke.)

More specifically, the assignment for both TPC and GA2:  the grade of the road has everything in the world to do with a trig function.  Which one? Why? Explain.  Use roads that you've seen or know about or find on line.  There's a couple different standards for handicap ramps (businesses vs private homes); find those if you'd like.  Go bananas on this one -- where else do you hear about grades?  What about the "angle of repose"?  What's that?  What about "railroad grades"?  Choose something that interests you; don't feel as though you need to cover absolutely everything, but DO cover the idea of what a "grade" is.   If you are one of those folks in GA2 fascinated by the number theory topic we touched on (Pythagorean Generators), you can choose to write on that instead of this whole idea.

GA2: Fractions in the Fast Lane: July 17, 2013, published August 19, 2013

"How did you happen to be so good with fractions," friends used to ask when I was in middle school.  Everybody knows everybody universally dislikes fractions.  For me, it was all about distance swimming.  I knew I could solve the world's problems during a long workout (though I'd forget the solutions to the world's most serious problems as I climbed out of the water); what I didn't know was how I was using swimming to solidify my working facility with fractions.  It was simple: as I swam 1,000 meters, I was constantly figuring out what fractions -- and what ratios were identical to the reduced fractions -- could represent how far I had swum and how much further I had to swim before I finished.  It started simply: if I swam 40 lengths in a 25 meter pool, then after 7 lengths, I was 7/40th done and had 33/40 to go.

Sometimes, however, I swam in the 20 meter YMCA pool and the numbers became different. I needed to focus and not just rely on memory.  I now had to swim 50 lengths to complete 1,000 meters.

My thinking soon became more complicated and required swifter calculations -- I moved to measuring what fraction of the swim I had completed for each stroke -- or even each partial stroke.

Bored with that, I began watching my teammates swimming in the neighboring lanes.  What were their ratios and how were their numbers different from mine?  At what points would we pass each other?

I long since moved away from my home town, stopped swimming, and became a math teacher. I forgot about fractions in the fast lane.

Then deep into middle age, I started swimming again.  And calculating fractions.  I kept this secret lest my lane-mates think me insane.

I don't always swim in pools.  There are lakes with cool fresh water, sunbeams that cut through the waves, and no visible bottoms. Plants grow through the water towards the source of the sunbeams, branching in infinitely smaller "Y" shapes at the same angles.  Bubbles surface and break into more and smaller bubbles from the depths; there are no numbers. Only fractals.  And chaos. And new things to think about.

Your blog: where do you use math in secret?  Or if you don't use math in secret, where might you start using math in secret or not in secret so you can increase your skills in math?