Literaturnachweis - Detailanzeige
| Autor/in | Skurnick, Ronald |
|---|---|
| Titel | A Classroom Note on a Sufficient, but Unsatisfied, Condition for Goldbach's Conjecture to Be True |
| Quelle | In: Mathematics and Computer Education, 45 (2011) 1, S.66-71 (6 Seiten)
PDF als Volltext |
| Sprache | englisch |
| Dokumenttyp | gedruckt; online; Zeitschriftenaufsatz |
| ISSN | 0730-8639 |
| Schlagwörter | Mathematical Formulas; Numbers; Number Concepts; High School Students; Mathematics Instruction; Validity; Mathematical Logic; Problem Solving; Theories; College Mathematics |
| Abstract | This classroom note is presented as a suggested exercise--not to have the class prove or disprove Goldbach's Conjecture, but to stimulate student discussions in the classroom regarding proof, as well as necessary, sufficient, satisfied, and unsatisfied conditions. Goldbach's Conjecture is one of the oldest unsolved problems in the field of number theory. One of the most attractive features of this well-known conjecture, which dates back to the year 1742, is that its statement is so simple that it can be understood by a high school student. Goldbach's Conjecture asserts that every even integer greater than or equal to 4 can be expressed as the sum of two (not necessarily distinct) prime numbers. In this article, the author presents a "sufficient" condition for Goldbach's Conjecture to be true. It is then observed that the Prime Number Theorem strongly suggests that this sufficient condition is, in fact, "unsatisfied." This leads to provide a counterexample (to the sufficient condition), which demonstrates that it has "not" been determined whether Goldbach's Conjecture is true or false. (Contains 4 tables.) (ERIC). |
| Anmerkungen | MATYC Journal Inc. Mathematics and Computer Education, P.O. Box 158, Old Bethpage, NY 11804. Tel: 516-822-5475; e-mail: macej@optonline.net Web site: http://www.macejournal.org |
| Erfasst von | ERIC (Education Resources Information Center), Washington, DC |
| Update | 2017/4/10 |
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