Are Random Triangles Acute or Obtuse?

Are Random Triangles Acute or Obtuse?

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Gilbert Strang
Professor of Mathematics
Massachusetts Institute of Technology
Cambridge, Massachusetts 02139 USA

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This learning video deals with a question of geometrical probability. A key idea presented is the fact that a linear equation in three dimensions produces a plane. The video focuses on random triangles that are defined by their three respective angles. These angles are chosen randomly subject to a constraint that they must sum to 180 degrees. One class period is required to complete this learning video, and the only prerequisites are a familiarity with geometry and an understanding of the equation for a plane, which is presented in the module. Materials needed for this lesson include blackboard and chalk. Optional materials include a cardboard box and colored paper. An example of the types of in-class activities for between segments of the video is: Ask six students for numbers and make those numbers the coordinates x,y of three points. Then have the class try to figure out how to decide if the triangle with those corners is acute or obtuse.

Instructor Biography

Professor Strang teaches Linear Algebra and Computational Science at MIT, and both of these classes are videotaped and available on MIT's OpenCourseWare He also writes research papers and textbooks on these subjects. Click here to read more about Professor Strang.

For Teachers

Additional Online Resources

Professor Strang’s Linear Algebra Class lecture videos

Wolfram MathWorld: Obtuse Triangle
An online discussion of the problem discussed in this learning video

Math Open Reference: Obtuse Triangle
A free interactive math textbook on the web. Initially covering high-school geometry

Interactive: Probability and Geometry
An interactive lesson connecting probability and geometry

Wolfram MathWorld: Geometry
Provides extensive resources for the study of geometry