Mathy Activities

Originally Posted 02-01-2012

Tomorrow involves several non-standard bits of work for me. UNI is hosting 31 prospective undergraduate students and their parents for the day at an event we call MathDay. Also, it is time for another math club meeting.

Math Day Recruiting Activity

A big part of math day is the salesmanship of some little activity workshops we run for the students. Last year’s was particularly successful so I am going to use it again. Now, the important thing is the performance, and last year, man, I was on: wit, charm, energy, humor. I hope it goes as well this year. the activity is fun enough on its own to survive no matter what, but it is simple enough that I can give it to you in two sentences.

First bisect a Moebius band to get a longer Moebius band (still one piece!). Now explore generalizations with different numbers of half twists or different types of cuts.

This is stolen adapted from an old Martin Gardner Scientific American column called Mathematical Games. It is fun, just weird enough that you have to try it yourself to see how it works, and straightforward enough that you can make a clear conjecture inside of forty-five minutes.

Math Club

I recently learned a neat theorem by John H Conway and Cameron Gordon (I think I am remembering that correctly) that says any embedding of the complete graph on six vertices into three dimensional space must contain a pair of linked triangles.

This is just plain awesome. I am still working on a plan, but it might involve some play-doh and shoestrings. Or maybe it should be pipe cleaners.

Anyway, both are good topics for engaging students. Use as enrichment or as a hook.

Outreach?

Another odd thing is that a local high school teacher had a student give a proof that 2=0 using complex numbers. He wrote the department, and somehow I got picked as the person to answer his plea for help.

It is a fun one, so I’ll just leave the argument here and let you puzzle it out.

Anthony’s Paradox

1+1 = 1 + \sqrt{1} = 1 + \sqrt{-1 \cdot -1} = 1 + (i) \cdot (i) = 1+ i^2 = 1 + (- 1)  = 0.

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