Things of Interest ?
by Siegfried "Zig" Herzog
started August 2013
I obtained my PhD in Mechanical and Aerospace Engineering from Cornell
University in 1985. After a post-doc at Leheigh University and
Penn State University I started my teaching career at the
Mont Alto campus of the
The Pennsylvania State University
After some 24 years of teaching courses in statics, dynamics, strength of
materials and thermodynamics
I decided to retire on a high note (Excellence in teaching award from the
Engineering at PSU in 2012) and co-authoring a paper in prime number theory
(accepted but not published yet) in July of 2013.
Below you find links to material which are partially related to my past work
and partially to my present hobbies. You may contact me on any of the subjects listed below. Comments, questions and suggestions are most welcome, feel free to use either the "Send a Note to Zig" link or my email address.
Courses I taught which have some type of web presence
- Cmpsc 201 (class material, programmin projects)
Computer Programming for Engineers Using C++ (class material, programming projects)
- ME 300 Engineering Thermodynamics (little class material, 15 computerized homework problems, some 50 sample exam problems)
- EMch 211 Statics (a rudimentary on-line text book with lots of solved and unsolved problems and web-based computer programs
- EMch 212 Dynamics (little class material, 13 computerized homework problems, some 50 sample exam problems)
- EMch 213 Strength of Materials (little class material, 13 computerized homework problems, some 50 sample exam problems)
On the Gaps of adjacent Prime Numbers
Although prime numbers have - as far as I know - no application in engineering
they are by themselves a fascinating subject area, at least to me. Get a list
of all prime numbers up to 10,000 here
Although there are some equations available which produce a large number of
prime numbers these equations cannot be used to predict prime numbers
A classical example, dating back to Euler, is the equation :
f(n)=n2 + n + 41
which produces prime numbers for each n
between 0 and 39 (inclusive)
but mingles primes and composite numbers for larger n in seemingly random fashion.
Already a casual observation of the first, let's say hundred, prime numbers reveals that they seem to thin out. Still, it can be proven easily that there are infinitely many of them, see here for a proof due to Euclid (300 B.C.).
Related to that is the question as to how many prime numbers exists
below a chosen value x. This is called the prime counting function,
most often denoted by π(x) or pi(x). An excellent and short treatise of
π(x) can be found at Chris K. Caldwell, How many primes are there, table, Values of pi(x) and
analytical functions which approximate π(x) at
Chris K. Caldwell, How many primes are there,approximations.
Having access to some computational resouces I participated in a research
project on prime numbers which resulted in an
article EMPIRICAL VERIFICATION OF THE EVEN GOLDBACH CONJECTURE AND COMPUTATION OF PRIME GAPS UP TO 4*1018 by
Tomás Oliveira e Silva, Siegfried Herzog and Silvio Pard published in
Math. Comp. 83 (2014), 2033-2060
Click here for more on prime numbers
and gaps between adjacent prime numbers
Linear Equation Systems Solver
Linear equations appear in all types of mathematical problems and general
solvers for them are frequently needed. Of course, mine cannot cover everything
particularily when it comes to efficiency. But the following has served me well
on numerous occasions.
A linear equation system solver
(up to 20 unknowns)
This was project connected to a trebuchet which was capable to throw a pumpkin
some 300 ft. After a few years of usage (once a year for maybe some 100 throws
each) the beam broke. There are two parts to this simulator. The first is a
animated display of the actual motion of the trebuchet for the case of a hinged solid-body counter-weight with the projectile sliding initially inside a
horizonatal shute. The user can supply any sensible choice of parameters.
The second part reflects a stress analysis which, at the moment, pertains
only to our trebuchet ( labelled Renfrew ).
My Trebuchet Simulator
Stirling Engines have fascinated me for a long time but I never found enough
time for this hobby. Follow the link below to find out what I have done sofar
which is mostly theoretical stuff. But some of it might be of interest
to the practioner as well.
Stuff on Stirling Engine
Math and other small puzzles
There is not much to be found here. In fact only one puzzle Grazing goat problem
Send a Note to Zig
Zig Herzog © 2014
Last revised: 02/05/16
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