Flexagons and Other Things Found While Looking for Schwinger Lippmann

While searching for journal articles on the Schwinger-Lippmann scattering rule last night, I came across the following.

Maybe We Let Quaternions Go A Little Too Easily
http://aapt.scitation.org/doi/abs/10.1119/1.1934944

Relation of quaternions to four dimensional rotations[2]

If you're into fringe physics, McIntosh worked for RIAS who dabbled in shall we say 'gravity control' in the 1950s.
RIAS Inc. of Baltimore[3]
RIAS on antigrav[4]

McIntosh did a significant amount of group theory work and went on to publish a survey of flexagons in 2003[pdf][5]. This brings us to the really cool flexagon stuff! First, watch the series of videos on hexaflexagons[10]!

Then, go read more about them at the American Mathematical Monthly[6] and Scientific American[7]. They were invented in 1939 and while Feynman didn't come up with the idea, he was involved.

from +Scientific American

Epstein again
The author that pointed out Israel Senitzky also wrote a paper on quantum mechanical scattering[8]. Interestingly, he's not associated with an institution and we find him in New York, NY. Reading up on him, it looks like he was at Columbia at the time. He wound up at the University of Wisconsin[9].

References
1. On Accidental Degeneracy in Classical and Quantum Mechanics
http://ajp.aapt.org/resource/1/ajpias/v27/i9/p620_s1

2. http://en.wikipedia.org/wiki/Rotations_in_4-dimensional_Euclidean_space#Relation_to_quaternions

3. http://en.wikipedia.org/wiki/Research_Institute_for_Advanced_Studies

4. http://en.wikipedia.org/wiki/United_States_gravity_control_propulsion_research#Research_Institute_for_Advanced_Study_.28RIAS.29

5. http://delta.cs.cinvestav.mx/~mcintosh/cellularautomata/FLEXAGONS_files/gonaflex.pdf

6. The American Mathematical Monthly, 64, (1957), "Flexagons"
http://www.jstor.org/stable/10.2307/2310544

7. Scientific American, December, 1956, "Flexagons"
http://www.nature.com/scientificamerican/journal/v195/n6/index.html

8. http://prola.aps.org/abstract/PR/v86/i6/p836_1

9. http://www.physics.wisc.edu/alumni/pdf/newsletter-spring2011.pdf

10. http://www.youtube.com/watch?v=VIVIegSt81k

Comments

The Valentine's Day Magnetic Monopole

There's an assymetry to the form of the two Maxwell's equations shown in picture 1. While the divergence of the electric field is proportional to the electric charge density at a given point, the divergence of the magnetic field is equal to zero. This is typically explained in the following way. While we know that electrons, the fundamental electric charge carriers exist, evidence seems to indicate that magnetic monopoles, the particles that would carry magnetic 'charge', either don't exist, or, the energies required to create them are so high that they are exceedingly rare. That doesn't stop us from looking for them though! Keeping with the theme of Fairbank[1] and his academic progeny over the semester break, today's post is about the discovery of a magnetic monopole candidate event by one of the Fairbank's graduate students, Blas Cabrera[2]. Cabrera was utilizing a loop type of magnetic monopole detector. Its operation is in...

Cool Math Tricks: Deriving the Divergence, (Del or Nabla) into New (Cylindrical) Coordinate Systems

Now available as a Kindle ebook for 99 cents ! Get a spiffy ebook, and fund more physics The following is a pretty lengthy procedure, but converting the divergence, (nabla, del) operator between coordinate systems comes up pretty often. While there are tables for converting between common coordinate systems , there seem to be fewer explanations of the procedure for deriving the conversion, so here goes! What do we actually want? To convert the Cartesian nabla to the nabla for another coordinate system, say… cylindrical coordinates. What we’ll need: 1. The Cartesian Nabla: 2. A set of equations relating the Cartesian coordinates to cylindrical coordinates: 3. A set of equations relating the Cartesian basis vectors to the basis vectors of the new coordinate system: How to do it: Use the chain rule for differentiation to convert the derivatives with respect to the Cartesian variables to derivatives with respect to the cylindrical variables. The chain ...

More Cowbell! Record Production using Google Forms and Charts

First, the what : This article shows how to embed a new Google Form into any web page. To demonstrate ths, a chart and form that allow blog readers to control the recording levels of each instrument in Blue Oyster Cult's "(Don't Fear) The Reaper" is used. HTML code from the Google version of the form included on this page is shown and the parts that need to be modified are highlighted. Next, the why : Google recently released an e-mail form feature that allows users of Google Documents to create an e-mail a form that automatically places each user's input into an associated spreadsheet. As it turns out, with a little bit of work, the forms that are created by Google Docs can be embedded into any web page. Now, The Goods: Click on the instrument you want turned up, click the submit button and then refresh the page. Through the magic of Google Forms as soon as you click on submit and refresh this web page, the data chart will update immediately. Turn up the:...

Copasetic Flow

Search This Blog