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Volume 4, Number 17A  -  April 1999 Discussions

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28 April 1999                                 Vol. 4, No. 17A


  This special issue of the Math Forum's weekly newsletter
  highlights recent interesting conversations on Internet 
  math discussion groups.

  For a full list of these groups with links to topics covered
  and information on how to subscribe, see:


  Replies to individual discussions should be addressed to
  the appropriate group rather than to the newsletter editor.

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                       APRIL SUGGESTIONS:

AP-CALC - the Advanced Placement Calculus mailing list, hosted 
by the Educational Testing Service (ETS) and archived at:
- Implicit Diff & Inverse Functions (16 Apr 1999)

 "One of the objectives calls for using implicit 
  differentiation to find the derivative of inverse 
  functions... Can someone point me to a resource for this 
  topic or explain it...?" - Rob Duncan

  Responses from list participants include examples,
  recommendations for textbooks, and a Web site, Cram Central: from Apex Publishing Company
  that has "a nice student tutorial on that subject under the 
  heading 'inverse functions'..." - Eileen Diggle
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GEOMETRY-PUZZLES, for interesting problems and conundrums that 
require only a knowledge of pre-college geometry, as well as 
discussions and solutions, hosted by the Math Forum at:

- Triangle Problem (9 Apr 1999)

 "Let ABC be a triangle, I its incenter and F its Fermat-
  Torricelli point. It is known that the Euler lines of ABC, 
  ABI, ACI and BCI concur in one point (The 'Schiffler point').
  Show that the Euler lines of ABC, ABF, ACF, and BCF concur 
  in one point too." - Floor van Lamoen

 "There are two interesting families of cubics associated with 
  a triangle, which I call the 'isotomic' and 'isogonal' cubics.
  The typical isotomic cubic has an equation that's a linear
  relation in YZ(Y-Z), ZX(Z-X), XY(X-Y) (where X,Y,Z are
  barycentric coordinates), and the typical isogonal one has 
  a similar one with X,Y,Z replaced by the trilinear coordinates 
  x,y,z. In each case, the cubic is determined by a 'pivot point' 
  whose coordinates specify the linear combination. - John Conway
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NUMERACY, for those interested in the discussion of educational 
issues around adult mathematical literacy, archived at:

- Looking for the "rightest" answers... (13 Apr 1999)

 "The Carpenter's apprentice exam uses 3.1416 for pi even
  though every text I've seen uses either 22/7 or 3.14. And of
  course my calculator has a nine digit pi... So that gives 
  each problem using pi at least four possible answers, all 
  fairly close within the thousands or so. (Unless it's a 
  'book' problem meant to work out to a whole number with 
  22/7...) Is there a preferred form of pi? You know how 
  students hate ambiguity... What do you say when students ask 
  which is more 'correct' for the perimeter of a triangle, 
  a+b+c or s1+s2+s3? And when the formula test is handed back 
  tomorrow I am going to have arguments that 4S really *is the 
  same* as s1+s2+s3+s4 or 2L+2W ... I'd appreciate comments 
  from survivors of the geometry wars..." - Lynne

 "This illustrates the interesting differences between ordinary 
  language and mathematical language and the confusion between. 
  It's a good opportunity to discuss this difference and explore 
  a solution. I am a little leery of teaching formulas per se. 
  Can they choose/use them in the appropriate situation that 
  doesn't use the words circumference, perimeter, or 'area of 
  a triangle'?" - Ron

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SCI.MATH, a discussion group focused on general and advanced 
mathematics that can be read as a Usenet newsgroup or on the Web:
- A Loophole In Cantor's Argument? (5 Feb 1999)
  There are over 200 messages in this thread, more than 70
  of them posted since April 15. The conversation began in
  February with a discussion of Cantor's diagonal proof of
  the uncountability of the set of real numbers:

 "...Before I propose an ordering of the set of all reals, let
  me say that it may not at first appear very interesting or 
  promising. The reason is that it is a countable union of 
  countable sets, is therefore countable, and can therefore be 
  placed into one-to-one correspondence with the set of all 
  integers. However, for reasons which I will explain shortly, 
  this may be less important than it seems. The ordering of the 
  set of all reals I propose is a list of aleph_0 groups each 
  containing aleph_0 reals..." - Mark Adkins 

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  We hope you will find these selections useful, and that you
  will browse and participate in the discussion group(s) of
  your choice.  

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