Fun with 3d printing

I acquired a resin (SLA) 3d printer recently, and have been working on my printing skills.  The idea is to build some helpful mathematics models, useful in geometry and topology classes.  I've always found this model useful when explaining Poincare duality.  It's the tetrahedron, together with the parts of the dual CW-complex that one can see from inside the tetrahedron.  

Isotopy in dimension 4

Four-dimensional manifold theory is remarkable for a variety of reasons.  It has the only outstanding generalized smooth Poincare conjecture.  It is the only dimension where vector spaces have more than one smooth structure.  The only dimension with an outstanding generalized Shoenflies problem.  The list goes on.  One issue that is perhaps not discussed enough is the paucity of theorems about smooth isotopy.    In dimensions 2 and 3, the Schoenflies and Alexander theorems are the backbone of all theorems about isotopy, allowing one to work from the ground-up.

News in 3d graphics software

Over the past several years, a few CAD packages developed on-line interfaces.  I'm thinking of Sketchup and TinkerCAD.   

Sketchup has historically been oriented more towards architechture and home layout.  TinkerCAD was intended as a baby version of AutoCAD, I imagine as something of a "gateway drug" to an expensive AutoCAD purchase. 

Why are mathematics departments so large?

Why are mathematics departments so large?   Isn't mathematics basically done?  Is there really any research left to do?

A university the size of U.Victoria probably would only have 5 or 6 mathematicians, broadly construed, if it only cared about mathematics research functionality. Mathematics research is alive and well in the world, and it has both short-term and long-term real-world implications.  But our societal interest in mathematics research does not warrant the number of faculty in our research institutions. 

Magnetic field around a conducting Moebius band

Here is another visualization from my course.  We are computing magnetic fields around conductors.  This is part of a demonstration of how (relatively easily) we can compute magnetic fields about fairly arbitrary conductors.  In this case, think of the Moebius band as an interval bundle over a circle.  The electric current is running the the direction of the base circle.  

More elementary stats derived from the VPD page

In the 30-day span of data I downloaded, Saturday appears to be the busiest day for the Victoria police.  

A breakdown of the Victoria Police department "crime types" for all incidents over the past 30 days.

This semester I've been enjoying teaching a course where we use Python.  I've been getting acquainted with its abilities to pull and parse data off the internet, and turn it into useful graphics.  The Victoria Police Department has an incident-report webpage.  I wrote a script to strip the crime data off the webpage and will ask my students to do some basic statistical analysis of the data.  Here is a teaser of what's to come.

Interactive Graphics - Python and Plotly

A completely different graphics engine for Python is called Plotly.   Aside from being a very slick package, the library makes the transition to using your graphics on-line as seamless as possible.  The plot below is an interactive rendering of a parametric surface in R3, a torus knot. You can zoom and rotate with your mouse.  The code to generate the plot was written in Python.

Interactive graphics - Python, SymPy and VisPy

One of my childhood jobs was for an engineering company.  This was back in the days before Matlab or Mathematica.  I would write software for this company (interestingly the company failed and was reincarnated as FlexPipe in 2001, the owners being the previous engineers), to compute numerical integrals to predict the pressure it should take to make their pipe explode, in various configurations.


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