College Math Teaching

August 19, 2016

A fun question concerning projections

Filed under: geometry, popular mathematics — Tags: — collegemathteaching @ 11:34 am

The semester is about to start. I decided to have some fun on Facebook. I took some office shots (yes, my office is messy) and decided to retouch the photos by adding joke photos from Facebook; I wanted to see which friends noticed (without being specifically notified). One did.



Of course, the color alone will give away which “on the wall” photos are genuine and which were put in (via Paint).

But a fun question is: if those photos were to be genuine, what size and shape would they be in real life (to appear the way that they do in those shots). One would give the genuine dimensions of the genuine photos on the wall to help the student solve the problem.

A more sophisticated 3-d version of the problem can be obtained from this cool video:

August 11, 2016

Post Promotion Summer

Filed under: editorial, topology — Tags: — collegemathteaching @ 12:02 am

This is my first “terminal promotion” summer. And while I have something that I have “sort of” written up…I just don’t like the result; it basically fills in some gaps in a survey article. But I think that my thinking about this article has lead me to something that I can add to the paper so that I’ll actually LIKE what I submit.

Then again, my quandary can be summed up in this tweet:


If I wait until I am absolutely in love with my work before I send it out, it will never get sent out.

Hopefully, I’ll have more material to add to this blog this semester.

What I am working on: equivalence classes of simple closed curves; these are one to one, continuous images of the unit circle in 3-space. The objects that I am studying are so pathological that these curves fail to have a tangent at ANY point. One of these beasts can be constructed by taking the intersection of these nested, solid tori.


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