Three-sided Cylindrical Dice

short die tall die

How can we construct a fair three-sided cylindrical die?

For example, a "short" cylinder will almost always land on one of the ends and rarely on the side. A tall cylinder will almost always land on its side and rarely on an end. How should we construct the die so that if we label the ends with "1" and "2" and the side with "3" each number will have an equal chance of coming up?

Our exploration was inspired by "Examining Cylindrical Dice" by Dustin L. Jones, The Mathematics Teacher. Volume 102, Issue 6, pages 420--424, published by the National Council of Teachers of Mathematics, February 2009.

The report linked below was written by the participating students.


Riverbend Community Math Center
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This work placed into the public domain by the Riverbend Community Math Center.