Archive for December, 2009

How would Michael Palin say “Quod erat demonstrandum”?

December 17, 2009

The letters QED (or the unabbreviated “quod erat demonstrandum” [“which is what was to be proved”]) are often used to indicate the end of a formal proof.  This longstanding tradition goes back to a style of proof writing, where the culminating sentence of the argument gives a recapitulation of the statement of the theorem; the QED places a stamp of finality on the discussion.

In modern typesetting, the QED has been largely replaced with typographic symbols; typically a solid or hollow rectangle or square is used to demark the end of the proof.  (The cynic in me wonders if these just serve as flags for when the reader should take up reading carefully again.)

How does one indicate the end of a proof in a classroom setting?  Often I will scribble out a square (or whatever symbol our textbook uses); sometimes I’ve written out “Q.E.D.”.  Often I’ll pause, then solicit questions and comments.

But apparently I much more frequently channel Michael Palin.

Today I gave a final exam in Real Analysis II.  This group of students has gotten to work with me on proofs for a full year, so they know my quirks and foibles better than most.

On the last page of the final, most of the students ended their last proof with the phrase:

“And there was much rejoicing.”

This isn’t a phrase I’ve consciously chosen to use in class, but it rings true enough as something I’m sure I *have* said on occasion.  But if it made this much of an impression on the students, I wonder if I use it all the time, not just occasionally.  Hmmm.

Come to think of it, it isn’t such a bad replacement for Quod erat demonstrandum.  Captures the feeling of a good solid proof, well-understood.  And it is much more evocative than a box.

An ode to Andreia Chaves

December 14, 2009

(To the tune of “The Christmas Shoes”. Sorry about that.)

It was almost exam time
Sum. Solve. Is this a prime?
Trying to find a good shape or two
Not really in a polygon mood
Then appeared right in front of me
As I surfed somewhat anxiously
The creativity that designers do
But these were mathematical
Artsy pairs of shoes

And these shoes weren’t worn or old
They had V+F=E+2 from heel to toe
Fit for show more than for play
And I couldn’t believe, but they made me say

Yes I wanna show these shoes
To my classes please
There’s origami
Which adds quite a bit of style

I’d better hurry now
My datebook says there’s not much time
You see, classes have met for quite a while
And I know these shoes will make them smile
Cuz those shapes look kind of beautiful
While everyone is studying tonight.

These shoes, designed by Andreia Chaves of São Paulo, Brazil, were featured on yatzer (found via cnet).    All photos are used with permission from the folk at yatzer (Thanks!)

Other functions for this curve?

December 13, 2009

I got a call this afternoon from Marc, a friend of mine from college in Minnesota who now lives back East and runs his own business. He was trying to find a model for a collection of functions, but couldn’t figure out what kind of function it would be.

The basic scenario was that the function should start at (0,0), increase rapidly to a point [say, (10,10)], and then slowly decrease.  The x-axis could be a practical asymptote, although it didn’t really matter since this would only be looked at in finite time.

My first thought was  surge function (something of the form Axe^{-Bx}), and sure enough that works.  But I was on Homework Patrol, so I handed it off to TwoPi, and he came up with xe^{1-0.1x} and \frac{80x}{(x+6)(0.01x^2+4)}.  Walphaing these shows that both work well:

This seemed to help.  So here’s what I’m wondering — are there any other simple functions that fit the bill?  Neither function is too complicated, but it would be fun to be able to share other examples of functions that rise quickly, but then that taper off after a while.  [I think the tapering should be more gradual compared to the climb, though I believe that can be controlled with more constants.

Fox News Fail

December 12, 2009

It really wan’t my intent to post three math fails in a row — indeed, the only intent was to post something, since the last month semester six months have been rather sparce, post-wise.  But then I saw an article on the Huffington Post which they got from Media Matters (which includes a great graphic and a video) and, well, another fail it is!

Here’s the scoop:  Rasmussen Reports posted the results of a poll about climate change that included the following question and answers:

3* In order to support their own theories and beliefs about global warming, how likely is it that some scientists have falsified research data?

35% Very likely
24% Somewhat likely
21% Not very likely
5% Not at all likely
15% Not sure

If you were going to summarize this, how would you do it?  Maybe combining categories, like this:

59%  Very or somewhat likely
26%  Not very or not at all likely
15%  Not sure

But that’s a little awkward, isn’t it?  So maybe you’d change the wording to emphasize the likely and not likely, and drop the people who are sure.  that leaves:

59%  Likely
26%  Not very likely

Hmmmm.  This is accurate enough, but to make it sound better, you might add back in the “Very likely” as a parallel to “Not very likely” [OK, you probably wouldn’t do that.  But let’s pretend you would.].  That would give

59%  Likely
35% Very likely
26%  Not very likely

And that, my friends, is how Fox News you do a poll.

As a follow up, Producer Lauren Patterson claimed, “We were just talking about three interesting pieces of information from Rasmussen….We didn’t put on the screen that it added up to 100 percent.”    Yeah, sure, that makes it all OK.

Creative Exams

December 11, 2009

Finals ended today — woo hoo! [This is the earliest they’ve ever finished, and I can’t say I’m upset.] In that spirit, here’s one of the latest from Fail Blog (similar to others I’ve seen, but this appears to be more recent).

epic fail pictures
see more Epic Fails

I’m not sure if the drawings help, but they certainly don’t hurt.

Ahhh, those holiday deals!

December 10, 2009

Isn’t it great how many places are giving such big discounts?  It’s not quite two for the price of three, but still…

epic fail pictures
see more Epic Fails

And to think, it’s still good for another month!