Commentary: Euclid’s Algorithm

 

            I created the original tutorial for a technology workshop for Wheelock faculty, where I was to discuss novel ways to use spreadsheets for teaching.  The faculty members were primarily not from technical fields, and I wanted them to learn some new mathematics using the spreadsheet.  We started by hand, and then most of us worked together, at computers and with me on the projector, to set up a spreadsheet, with those who wanted to working on their own.  The “old” version of the algorithm (as written in Euclid) is easier for novices to understand, and it is very easy to set up on a spreadsheet.  The tutorial handout is a step-by-step guide to setting up the algorithm on a spreadsheet.

            I prefer to have students figure out how to set up the algorithm on the spreadsheet themselves, however (see activity link below).  I like the way the spreadsheet makes the long version of Euclid’s Algorithm “practical.” 

            I have used variations of the activity in several courses at different levels.  Students have not seen the algorithm before, and most appreciate it, although only the more advanced students understand the full justification for why it works  it’s fairly easy to see that the any common factor of the two starting numbers divides the final result, but harder to see why the algorithm produces the greatest common factor (and even harder to motivate some students to see the need for such a proof!).  The activity is a nice lead in for talking about what an algorithm is.  7/05

 

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