Thursday, January 12, 2017

Math Stuff From Today

If you want to learn about so-called imaginary numbers, you could do a lot worse than watching the thirteen short videos from Welch Labs (the first is here).  I've watched only the first 11 so far, and I'm still not convinced that the parabola graphic in Video #1 is correct, but my department chair--who, incidentally, turned me on to these videos--assures me that I'll be convinced after I've watched the last one.  Anyway, if you're at all interested in the so-called imaginary numbers, then give the videos a watch.  I thought it interesting how they showed multiplication of complex numbers and, by extension, DeMoivre's Theorem.  The integration of algebra and geometry was exceptional.

And completely unrelated.... Yesterday in pre-calculus I introduced converting from degrees/minutes/seconds to decimal degrees, and vice versa.  Here is a paraphrase of the class starter problem I gave today:

Prior to 1969, Great Britain didn't use a decimal system for money like they do (and almost every other country does) today.  Their system was:
12 pence = 1 shilling
20 shillings = 1 pound
If an item cost £3 5s 4p, how many decimal pounds did it cost?
No, pre-decimal British money has nothing to do with angles, but the method of calculation is the same as that of degrees/minutes/seconds to decimal degrees.  I just wanted to see if my students could make the connection, and to my delight, most did.

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