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 Discussion: All Topics Topic: Java Applet - AGM inequality Related Item: http://mathforum.org/mathtools/tool/632/

 Post a new topic to the tool: Semicircle and Arithmetic, Geometric mean discussion

 Subject: Java Applet - AGM inequality Author: jon Date: Mar 15 2004
http://www.ies.co.jp/math/java/misc/mean/mean.html

This is a really well done applet.  It looks and moves smoothly.  And it uses
Java to provide a nice manipulative to the "proof" of the AGM inequality.
However, as a student I'd be very put off by this.  I don't think I'd really be
able to see the connection here unless there was some more guidance in
exploartion questions. The 3 steps they give you in exploring the inequality are
fairly basic.  The first one asks to figure out how they got the length of the
perpendicular to be sqrt(a*b) which is certainly important as that length
represents the geometric mean between the values of "a" an "b".  The second part
asks the student to consider when PH = sqrt(ab) by moving the dot around.  And
the third step again asks the student to "consider" a+b/2 > sqrt(ab).  I think
it's nice that the applet doesn't outright say what the student's supposed to
learn.  But for proof type manipulatives it's better for there to be more
structured questions and exploratory statements like, what do you notice about
the relationship between the length of a and b when sqrt(ab) , a+b/2.