RF Cascade Workbook

Copyright

1996 -
2016

Webmaster:

Kirt
Blattenberger,

BSEE - KB3UON

RF Cafe began life in 1996 as "RF Tools" in an AOL screen name web space totaling 2 MB. Its primary purpose was to provide me with ready access to commonly needed formulas and reference material while performing my work as an RF system and circuit design engineer. The Internet was still largely an unknown entity at the time and not much was available in the form of WYSIWYG ...

All trademarks, copyrights, patents, and other rights of ownership to images and text used on the RF Cafe website are hereby acknowledged.

My Hobby Website:

AirplanesAndRockets.com

to Find What You Need.

There are 1,000s of Pages Indexed on RF Cafe !

The January 2016 issue
of *Scientific American* ran an article by Clara Moskowitz titled "Elegant Equations"
that presented a few prints from "The Concinnitas Project"
which "...is a collection of ten aquatints produced from the contributions of ten mathematicians and physicists in response
to the prompt to transcribe their 'most beautiful mathematical expression.'" The renowned mathematicians and scientists
who contributed to the project are Michael Atiyah,
Enrico Bombieri,
Simon Donaldson,
Freeman Dyson,
Murray Gell-Mann,
Richard Karp, Peter Lax, David Mumford,
Stephen Smale, and
Steven Weinberg.

My personal favorite is "Ampère's Law," by
Simon Donaldson, because it incorporates a simple line drawing along with the familiar equations. It brings back memories
of sitting in electromagnetics class at the University of Vermont watching my seriously brilliant professor
(no kidding),
Dr. Kenneth Golden, draw boundary value problems on the chalkboard and write out formulas and proofs
- all from memory. Aside: Dr. Golden always had an office full of students during office hours, during which he would work
out any problem in the text book (*Field
and Wave Electromagnetics*) as easily as most of us perform simple addition.

Next in order of most liked is "Newton's Method," by Stephen Smale. I remember learning about Newton's Method in a differential equations class, even though, technically, it is not itself a differential equation. Newton's Method (Wikipedia) provides a means of estimating successively closer approximations to the roots (or zeroes) of a real-valued (i.e., non-imaginary) function. You begin with a 'best guess' and proceed with calculations. As with most methods of convergence, this is fraught with traps that could cause the result to eventually attempt to divide by zero, or go off in a completely erroneous direction. It has been the subject of much attention.

Richard Karp's entry of "P Versus NP" immediately reminded me of Charlie Epps, the boy genius mathematician in the television
show *NUMB3ERS* whose goal in life was to solve
the P = NP quandary. I can solve it for the trivial case where N = 1 ;-)

Surprisingly, Maxwell's Equations was not chosen by any of the ten participants.

As the unwilling victim of societal sensitivity after being constantly bombarded with messages of how my type - white, heterosexual male - is responsible for all the world's evils, I feel duty-bound to point out that unless one of these ten mathematicians and scientists is self-identifying as otherwise in order to gain access to Target bathrooms, all are, well, old white guys.

Bob Feldman regarding The Concinnitas Project: "The portfolio draws its name from a word famously used by the Renaissance scholar, artist, architect, and philosopher Leon Battista Alberti (1404-1472) to connote the balance of number, outline, and position (in essence, number geometry, and topology) that he believed characterize a beautiful work of art."

These items are an archive of past Topical Smorgasbord items that have appeared on the RF Cafe homepage. In keeping with the "cafe"
genre, these tidbits of information are truly a smorgasbord of topics. They all pertain to topics that are related to the general engineering
and science theme of RF Cafe. *Note: There is also a huge collection of my 'Factoids' (aka '**Kirt's Cogitations**') that might interest you as well.*

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Posted May 16, 2016