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4 comments on “Pythagoras and the Pyrenees ; Performance Enhancing Math”

Pythagoras and the Pyrenees ; Performance Enhancing Math

This image and its ilk bothers me to no end. This is a profile of the 9th stage of the Tour de France*.

(image adapted from letour.fr)

So I had this simple little post in mind about the Tour de France and biking and elevation and distance and it would wrap up neatly into a little Pythagorean Theorem lesson. I start looking around for nice little diagrams much like this one, showing the distance and elevation. The idea was going to be simply, “find the absolute distance the bikers travel in this particular stage.”

But it turns out these diagrams are a sham. An absolute sham. You see, the x-axis already does represent the absolute distance. Take this stage, for example. Above is the “cross section” of the stage. And here’s the actual route.

Note the exact same distance peddled. So x-axis is in actual distance peddled, not simply the horizontal distance traveled, as any proper diagramer should do. I suppose it’s more helpful for the bikers to know the absolute distance they have to travel, but it’s …. it’s….. it’s… just wrong. In retrospect, I did sort of think these slopes seemed a tad steep….

So we have a new task.

0 comments on “‘Groundhog Day:’ How long has Bill Murray been in Punxsutawney? (Part 2)”

‘Groundhog Day:’ How long has Bill Murray been in Punxsutawney? (Part 2)

Our celebration of Groundhog Day and Groundhog Day continues with our second question about Phil and his time spent in Punsutawney.

Artifact

This scene from Groundhog Day.

Guiding Questions

  • How long has Bill Murray (“Phil”) been practicing throwing cards into a hat?
  • Has Phil spent more time throwing cards into a hat than you’ve spent in Math class this year? Your entire high school career?
  • How good can you get at throwing cards into a hat after practicing for, say, 5 minutes? Can you make three in a row?

Solution

Rita: It would take a year to get good at this.

Phil: No. Six months. Four to five hours a day and you’d be an expert.

6 months = about 180 days.

180 days x 4 hours/day = 720 hours.

180 days x 5 hours/day = 900 hours.

Depending on the length of your school calendar and class periods, students are probably in Math class for about 200 hours/year. So that would be a “no” on Math-in-a-year vs. Phil-with-a-hat. But a “possibly” to Math-in-a-high-school-career vs. Phil-with-a-hat.

1 comment on “‘Groundhog Day’ “I’m a god” scene solution”

‘Groundhog Day’ “I’m a god” scene solution

Here’s my attempt at a solution to the previous post on Groundhog Day.

In order for Bill Murray (“Phil”) to convince Rita and allow for Rita’s peppering of questions, we have to assume that Phil knows everyone in the restaurantIt’s tough to get a beat on the number of people in the restaurant, but it’s a lot. I’ll start counting, but then we may have to fudge the numbers a little bit.

1 comment on “‘Groundhog Day:’ How long has Bill Murray been in Punxsutawney? (Part 1)”

‘Groundhog Day:’ How long has Bill Murray been in Punxsutawney? (Part 1)

Happy Groundhog Day everyone! Brief synopsis of Groundhog Day in case you didn’t know: Bill Murray is trapped in the same, repeating day in perpetuity.

How long Murray has been trapped is a question that has plagued mankind since the early 1990’s. It’s never directly addressed in the movie, it’s just hinted that it’s a long, long time. Probably months, possibly years.

Artifact

Let’s take this scene, for example.

How many days do you think it took Bill Murray to adequately retrieve and retain enough information to convince Rita that he is, in fact, a god?

Guiding Questions

  • How many people did Bill Murray discuss?
  • How many people are in the restaurant?
  • How many times would it take to know all that stuff about them?
  • How many times through would it take to get the timing on that crash of the tray dropping?

Suggested Activities

Some of these questions can be observed from the video. Some of these questions probably have to be estimated. But then, some could be investigated by your students. Think of all those “getting to know you” activities you put at the start of the year. Couldn’t we recreate something like that with this scene? Couldn’t we investigate “how many conversations does it take before you know enough details to describe the person well?”

Or couldn’t we investigate how many times before we could know exactly when an event will occur (the tray dropping)? I mean, don’t we do that in rewatching movies all the time?

5 comments on “Is there anything cooler than a math tattoo? (A: yes, pretty much everything)”

Is there anything cooler than a math tattoo? (A: yes, pretty much everything)

As I mentioned last time, the Pythagorean Theorem is a difficult concept to have students discover intuitively. So we’re focusing on it specifically this week. If you have any activities or ideas, please let me know. Or tweet it to me.

Here’s one sent in by Kevin.

========================================

A math nerd (Let’s say her name is Tara) decides that she is going to get a tattoo, and she draws up the following design for the artist to put on her back:

The colored ink costs $3 per square centimeter.  Outlining in black is free if the color costs $150 or more.   If the color is less than $150, then black outlining costs 50 cents per cm.

Tara wants those squares to form a right triangle like above, where the vertical leg is 5 cm long, and the horizontal leg is 7 cm long.

How much will the tattoo cost Tara?   Make sure to write out all of your calculations.

4 comments on “The Problem With Pythagoras”

The Problem With Pythagoras

And I’m not talking about the fact that he was a math cult leader. The Pythagorean Theorem is a tough one to teach in a “student-driven” or “discovery” fashion. It’s not very intuitive. It’s not like a high school student will be walking along one day, see a ladder propped up against a building and go,

Aha! A²+B²=C²!

This is ironic considering how widely used it and its parent, the Law of Cosines may be applied. So under the suggestion of a colleague, we’ll be looking at Pythagorean Theorem explicitly for the next couple posts. If you have any awesome ideas or stuff that your students have enjoyed in the past, please comment below or email me.

Oh look, someone left this random ladder resting against this random brick wall. Hold on guys while I calculate B!
1 comment on “Congressional seating for SOTU and Discrete Math”

Congressional seating for SOTU and Discrete Math

Remember when in elementary school when teachers would instruct you to sit “boy-girl-boy-girl?” Well, it appears as if the United States Congress needs to be reprimanded for their childish behavior and must sit “Democrat-Republican-Democrat-Republican.” You see, Colorado Senator Mark Udall made a proposal that during the 2011 State of the Union (SOTU) speech members of congress would sit amongst members of the opposite party. This is in contrast to previous SOTU addresses where the house of congress was firmly divided and after each line half of the house would cheer like their favorite team is trying to make a crucial 3rd down stop and the other half would sit on their hands and scowl. So members of congress accepted Udall’s proposal and immediately members of congress began trying to decide whom to sit next to so they could appear bi-partisan but so as not to sit next to anyone that’s an anathema to that politician’s base supporters (Seriously, they are children).

Anyway, as you may also know, Democrats lost a lot of seats in the 2010 mid-term elections after four years of steady gains. For the 2011 SOTU there were 242 Republicans (Rs) and 193 Democrats (Ds) in the House of Representatives; 53 Ds (and Independents who caucus with the Democrats) and 47 Rs in the Senate. As far as I know, the Senate and Congress sit together during the SOTU, so that’s a total of 289 Rs and 246 Ds.

So upon hearing that Ds and Rs were to sit together at the 2011 SOTU, I wondered a couple things:

  • Is it possible for every member of congress to sit next to a member of the opposite party?
  • If it is possible, how lopsided would the party split have to be before it becomes impossible?

I was hoping this wouldn’t be a simple discrete math problem. And as luck would have it, it isn’t (at least, I don’t think it is). Behold the floor-plan of the House of Representatives.

(note: not actually the floor plan of House of Representatives. At least I don’t think it is. And it certainly isn’t the seats used for the SOTU seeing as there are more members of congress than seats in this diagram. If anyone out there can find a better, more-correct diagram of the seats of Congress during a SOTU please email me. Below, I’ll start out using the entire congress, but eventually I’ll switch to just the House, and then I’ll declare that it doesn’t really matter.)

What a wonderful disparity of seats! There are rows of 15 and rows of two! There are things called the “Republican and Democratic Committee Tables”. And I’ve always wanted to know where the Tally Clerk sits.

So here’s how I would produce this to students.