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Unsolved Haiku, Scott W. Williams
Unsolved Haiku, Scott W. Williams
Journal of Humanistic Mathematics
This poem describes the still unsolved 1937 conjecture of Lloyd Collatz: Do repeated applications of the algorithm described yield the number 1?
The Genesis Of A Theorem, Osvaldo Marrero
The Genesis Of A Theorem, Osvaldo Marrero
Journal of Humanistic Mathematics
We present the story of a theorem's conception and birth. The tale begins with the circumstances in which the idea sprouted; then is the question's origin; next comes the preliminary investigation, which led to the conjecture and the proof; finally, we state the theorem. Our discussion is accessible to anyone who knows mathematical induction. Therefore, this material can be used for instruction in a variety of courses. In particular, this story may be used in undergraduate courses as an example of how mathematicians do research. As a bonus, the proof by induction is not of the simplest kind, because it …