## Monday, April 5, 2010

### 6 Divided By Pi^2 and Relatively Prime Integers - A Video Derivation

The current post presents a non-rigorous video derivation of a formula in mathematics which might create 'shock and awe' in kids of all ages. Oh, alright --  in people like me! This 3-part video is the followup to the post from March `16th -- Pi Day, More Videos on Counting, etc...

The following description comes from the YouTube Channel, MathNotationsVids:

Designed for anyone who has a passion for mathematics, this derivation of a classical result in math is suitable for advanced middle schoolers through undergraduate math. Further, teachers may want to show this to Math Clubs/Teams. This 3-part video builds on results from previous videos, is related to a post on MathNotations and is dedicated to the "Greatest Teacher in America" -- Prof. Jaime Escalante who passed away a few days ago.

Part I

Part II

Part III

• I hope you will see in these videos a central theme beyond the content involved -- a fundamental heuristic in teaching mathematics: When introducing an abstract concept or in deriving a formula or theorem or rule, avoid heavy symbolism and work with simple concrete numerical cases before generalizing results. I believe this has validity at all levels of math instruction.
• This topic ties together so many apparently unrelated topics in mathematics in a wondrous and surprising way. Perhaps it will inspire a budding mathematician as it did me...
• Visit my YouTube channel (see above) and please comment on these if you feel you want to see more. They are fairly labor-intensive (do you really think I'm speaking extemporaneously!) but they are worth it if someone enjoys them. The quality of the videos can still improve much more but this is just a beginning...

"All Truth passes through Three Stages: First, it is Ridiculed...
Second, it is Violently Opposed...
Third, it is Accepted as being Self-Evident."
- Arthur Schopenhauer (1778-1860)

#### 1 comment:

Jeff said...

Dave, off topic, but I was hopeful you could help. I'd like to figure out the odds that two consecutive numbers will come up in a lottery drawing involving 44 total numbers and six chances. Numbers are drawn from an urn; their order doesn't matter. Thanks!!!!

Jeff