# The Broken Stick Experiment: Triangles, Random Numbers and Probability

Richard C. Larson
Mitsui Professor of Engineering Systems
Massachusetts Institute of Technology
Cambridge, Massachusetts 02139 USA

Lesson vetted and approved by CPALMS

This learning video is designed to develop critical thinking in students by encouraging them to work from basic principles to solve a puzzling mathematics problem that contains uncertainty. One class session of approximately 55 minutes is necessary for lesson completion. First-year simple algebra is all that is required for the lesson, and any high school student in a college-preparatory math class should be able to participate in this exercise. Materials for in-class activities include: a yard stick, a meter stick or a straight branch of a tree; a saw or equivalent to cut the stick; and a blackboard or equivalent. In this video lesson, during in-class sessions between video segments, students will learn among other things: 1) how to generate random numbers; 2) how to deal with probability; and 3) how to construct and draw portions of the X-Y plane that satisfy linear inequalities.

View a "BLOSSOMS Extra," a PowerPoint audio lesson on discrete vs. continuous random variables as applied to the Broken Stick Problem. (click here to open page)

Watch three animated experiments (See "For Teachers" tab)

Dr. Larson's specialty is Operations Research, an interdisciplinary field that uses mathematics and the scientific method to improve decision making in industry and government.

Blog by "Bill the Lizard" on the Broken Stick Experiment.
http://www.billthelizard.com/2009/07/broken-stick-experiment.html

Extension of the Broken Stick Experiment by "Bill the Lizard", Obtuse Triangles.
http://www.billthelizard.com/2009/08/broken-stick-revisited_25.html

Web-based animated solution to the Broken Stick Problem
http://web.mit.edu/urban_or_book/www/animated-eg/stick/f1.0.html

Section 2.1 of the book, Urban Operations Research, available on the web
http://web.mit.edu/urban_or_book/www/book/chapter2/2.1.html

Explores reasons for studying math and practical applications of mathematical ideas
http://openlearn.open.ac.uk/course/view.php?id=1610

An interactive lesson connecting probability and geometry
http://www.shodor.org/interactivate/lessons/ProbabilityGeometry/

Presents and solves another probability puzzle
http://mathworld.wolfram.com/BuffonsNeedleProblem.html

Provides extensive resources for the study of Probability
http://mathworld.wolfram.com/topics/Probability.html

Provides extensive resources for the study of Geometry
http://mathworld.wolfram.com/topics/Geometry.html

MIT’s OpenCourseware: Introduction to Probability and Statistics
http://ocw.mit.edu/OcwWeb/Mathematics/18-05Spring-2005/CourseHome/index.htm