A walk down memory lane

I just found a page on "How to Find a Formula for a Set of Numbers".  It's a cool little procedure for taking a series, like:

2, 8, 9, 11, 20

and producing a polynomial to give you the next ones in the series, like:

n³- 17/2 n²+ 49/2 n - 15

where n is the term number, starting from n=1.  Try it out!  Anyway, it was a method I learned in high school math league, and thought it was so cool I wrote a BASIC program on the old TRS-80 computers to do it.  I had forgotten how to do it, and it was fun to see it again.  I particularly liked the comment on the page:

"""If someone gives you the sequence, say, "1, 4, 9, 16", you could run them through the above process and get the answer that the person is probably looking for: the rule is n² so the next value is 25. But you could also invent any number as the next number in the sequence, say 42, and come up with a rule for "1, 4, 9, 16, 42". Feel free to work it out. It comes out to:

 

17/24 n⁴ - 85/12 n³ + 619/24 n² - 425/12 n + 17

and the next term is then 121.

So if you want to be obnoxious, the next time you are given a quiz of "find the next number in the series" problems, just pick any number you like and fill it in, and you'll be completely correct. You'll probably get a failing grade on the test, but you can enjoy the smug satisfaction of knowing you were right."""

I knew a kid who, because of a ridiculous fluke, had to redo some of his middle-school competency tests in high school.  So, when presented with a series like 2,4,6,8,... he did this on a test (and yes he did fail the test and have to redo it).  He was also shown a number of clocks, and asked what time does this show, and for all of the answers put "analog time".

Power UnBalance

I love watching infomercials, but always wonder how much the sellers are exaggerating.  Take this infomercial for the "Power Balance" bracelet, which is claimed to increase balance and coordination:

http://www.youtube.com/watch?v=A_Ow-ZGMy5o

Now, go to this link which shows you how it actually works:

http://www.youtube.com/watch?v=Piu75P8sxTo

Make sure to watch the whole thing, because they give away the "trick" near the middle.  It is useful to go back afterward and watch the first one, now that you know the trick.

The real question, then, is: what should you do if you know a friend is considering buying this, or worse, has already bought it?  When I showed these videos in my class, I was told that the football team had purchased them already.  When some of my students presented them with the evidence, their response was that they didn't care whether it worked or not.

Astounding!