Hi, r/math! After lurking about for quite some time in this subreddit, I finally mustered up the courage to post on this subreddit. A bit of background: I am a Computer Science Engineering undergrad who wants to make the switch into pure mathematics. I want to do an independent study but unfortunately, I cannot find a mentor. The professors at college aren't really too keen on helping (blaming it on the bureaucracy). I am by now, comfortable in Real Analysis, Linear Algebra, Graph Theory, Group Theory and some Topology. I am really keen on learning, and I can really devote time to grasping new topics.
Earlier, I had thought of a problem, but I am really stuck on formulating the problem mathematically. The problem goes as follows:
Suppose, I have a string dipped in paint. Now I place that string onto a piece of paper arbitrarily and pull one end of the string along a straight line on the paper. (Note that this straight line is fixed for all such trials.) What are some properties of the geometry so traced out by the paint-smeared string, that remains invariant no matter how I place the string?
Here is a YouTube video for a rough idea of string paintings.
I am, however, open to other project ideas that others may suggest. Thanks in advance!
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from math https://ift.tt/2qWryxt
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