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I'm looking for a good topic to base my presentation on (length: 15-20 mins). I'm a freshman mathematics student, and my audience won't be skilled in mathematics beyond high-school maths. I've been looking all over, but I can't seem to find an inspirational subject - most are quite worn out. I'd love for it to be something related to topology or non-euclidean geometry. It doesn't matter if it gets somewhat abstract; I'll be able to tackle the pedagogy part. I'm just mostly out to make my audience see some interesting things in mathematics and make them think about it.

I'd love it if somebody would be so kind as to help me out here!

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  • $\begingroup$ The projective plane and the Poincare Disc should give you plenty to talk about and provide some decent pictures. I think there is a GeoGebra file out there too with tools to investigate the Poincare disc. $\endgroup$ – Paul Nov 25 '14 at 11:32
  • $\begingroup$ @Paul Thanks, the Poincare Disc seems like a great suggestion! I'm afraid the it's a bit too heavy on the mathematics though; do you have any thoughts/input on that? $\endgroup$ – Hend Nov 25 '14 at 11:37
  • $\begingroup$ The story of Gauss measuring triangles on the Earth's surface, in the kingdom Hannover. imdb.com/title/tt1571401 $\endgroup$ – mvw Nov 25 '14 at 11:37
  • $\begingroup$ It would help if you told us which subjects are "worn out", so we don't suggest topics you have already rejected. Are Mobius strips "worn out"? Knot Theory? classification of surfaces? Euler's $V-E+F$ formula? $\endgroup$ – Gerry Myerson Nov 25 '14 at 12:09
  • $\begingroup$ Between the projective plane and the Poincare disc you could talk about what "point" and "line" might mean without doing any algebra at all really. $\endgroup$ – Paul Nov 25 '14 at 12:10
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Knot Theory should be a winner. Here are some notes by a colleague, although you'll probably want to look at the chapter before this one to see where it's coming from.

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Let me recommend the book, Experiments in Topology, by Stephen Barr. You think the Mobius strip is a worn-out subject? Read Barr's chapter on The Shortest Mobius Strip, it might change your mind. Lots of other good stuff in that book.

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