Mike Raugh Michael Raugh

  Mike Raugh

   Mathematician

   Email: auranteacus at gmail com

   Brief Professional Bio

Recent Activity

Three talks resulted from an effort to find out who first solved the catenary problem: find the curve of a freely hanging chain. Leibniz and Johann Bernoulli independently published the first solutions in Acta Eruditorum 1691. Leibniz presented his solution as a classical Euclidean construction without an explanation of how he discovered it. The following three talks about his construction represent the evolution in my attempts to understand how Leibniz could have arrived at his solution. In the culminating talk of April 13 I present his analysis as disclosed in a private letter to Rudolph Von Bodenhausen made known to me by Sigmund Probst of the Leibniz Archive at the Göttingen Science Academy.

In reverse-chronologic order:

2017 (April 13) The Leibniz Catenary, an invited talk for the Dartmouth Mathematics Colloquium. In a private letter, Leibniz explained the analysis he used to arrive at his geometric construction of the catenary. He wrote: ``Let those who don't know the new analysis try their luck!'' This talk presents his elegant construction and analysis. Paradoxically, the construction isn't possible but it doesn't really matter!

2017 (January 4) The Leibniz Catenary Construction: Geometry vs Analysis in the 17th Century, an invited talk for the Special Session on the History of Mathematics at JMM 17 in Atlanta. This talk positions the publication of Leibniz's construction at the time when mathematicians were turning away from Descarte's dictate to present curves as geometric constructs toward analytic presentations. Leibniz played it both ways: he published a construction that could only have been derived using calculus but did not disclose the derivation publicly.

2016 (July 6) Talk for RIPS Program at IPAM: How did Leibniz Solve the Catenary Problem? A Mystery Story.

Turned out not to be a mystery after all! As I learned before the talk of January 4, Leibniz explained his solution in a private letter to Rudolph Von Bodenhausen of 1691 noted in the talk of Jan 4, 2017 and explained fully in the talk of March 13. (See also supplementary notes.) This talk sets forth an independent solution that demonstrates directly how the hyperbolic functions can be easily discovered at the heart of the catenary problem.

Previous Invited Talks

2014 A straightforward technique using integration to derive the Bernoulli Summation Formula, for the 29th LACC High School Math Contest, March 22.
2013 The Real Numbers are Not Real:, The Innumerable Infinities of Georg Cantor, March 16 at Los Angeles City College Math Contest.
Also presented to UNM Math & Stats Club on 3/8/2013. See the related Problematic Four Bugs ProblemOr Reality vs the Continuum.
2012 For New Mexico Math Contest of Feb 4: Archimedes' Law of the Lever and How He Used it to Deduce the Volume of the Sphere: Poster, Talk
(Repeated at Agilent Technologies Inc in Santa Clara at request of Geront Owen, 8/12/2013)
2012 What was on Top of Archimedes' Tomb?, Mar 2 at 27th Los Angeles City College Math Contest (abreviated version of the New Mexico Math Contest talk)
2010 The Innkeeper's Problem and Tale
2009 Irrationality of pi, with companion notes on Transcendentality of e
2008 How do you know what time it is?
2007 Hey, who really discovered that theorem!
2006 Eigenvalues and Eigenvectors, a chalk talk, first talk in a series for the Los Angeles City College High School Math Contest

2001–2015 Institute for Pure and Applied Mathematics (IPAM) at UCLA
Program director for Research in Industrial Projects for Students (RIPS)

On August 21, 2015 I concluded my fifteenth and final summer as director of the RIPS program at IPAM, a National Science Foundation's institute located at UCLA.

I worked with IPAM staff and the late Robert Borrelli of Harvey Mudd College to create the RIPS program in 2001, and then to continue developing the program over the fifteen summers of my directorship. I enjoyed working with the many students and academic mentors who participated in RIPS over all those years.

My approach to managing the RIPS program, was presented to the panel Starting and maintaining a student industrial research progam in the mathematical sciences at the MAA's MathFest of Aug 4, 2007 in San Jose, CA.

RIPS continued in the summer of 2016 under the directorship of the talented Spanish mathematician and teacher Prof. Susana Serna of the Autonomous University of Barcelona. Prof. Serna had been an academic mentor for RIPS teams for the previous eight summers.

Some write-ups of mathematical topics

A miscellany to include lecture notes, drafts and reminiscence

Some activites in mathematics

2011 I participated in review panels for the NSF and for the S. -T. Yau High School Mathematics Awards.

2007–present, Instructor at the LACES Calculus Camp (four days in April), the creation of Robert Vriesman, Chairman of the Math Department at the LACES magnet school in Los Angeles. See the 2012 Calculus Camp video by LACES student Blake Simon.


Informal

Photos and Slide shows


(Last modified May 16, 2017)