### Volume 4, Number 17A  -  April 1999 Discussions

 ``` 28 April 1999 Vol. 4, No. 17A THE MATH FORUM INTERNET NEWS - APRIL 1999 DISCUSSIONS 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: http://mathforum.org/discussions/ Replies to individual discussions should be addressed to the appropriate group rather than to the newsletter editor. ______________________________ + ______________________________ APRIL SUGGESTIONS: AP-CALC - the Advanced Placement Calculus mailing list, hosted by the Educational Testing Service (ETS) and archived at: http://mathforum.org/epigone/ap-calc/ - Implicit Diff & Inverse Functions (16 Apr 1999) http://mathforum.org/epigone/ap-calc/zydwahblel/ "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: http://www.cramcentral.com/ from Apex Publishing Company that has "a nice student tutorial on that subject under the heading 'inverse functions'..." - Eileen Diggle ______________________________ + ______________________________ 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: http://mathforum.org/epigone/geometry-puzzles/ - Triangle Problem (9 Apr 1999) http://mathforum.org/epigone/geometry-puzzles/skahvelnerd/ "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 ______________________________ + ______________________________ NUMERACY, for those interested in the discussion of educational issues around adult mathematical literacy, archived at: http://mathforum.org/epigone/numeracy/ - Looking for the "rightest" answers... (13 Apr 1999) http://mathforum.org/epigone/numeracy/yuntwixwix/ "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 ______________________________ + ______________________________ SCI.MATH, a discussion group focused on general and advanced mathematics that can be read as a Usenet newsgroup or on the Web: http://mathforum.org/epigone/sci.math/ - A Loophole In Cantor's Argument? (5 Feb 1999) http://mathforum.org/epigone/sci.math/gronjangwherd/ 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 ______________________________ + ______________________________ 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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