9860

Obtuse Random Triangles from Three Parts of the Unit Interval

Two points are chosen at random in the unit interval. From the resulting three parts, we try to form a triangle. If a triangle can be formed, we are interested in whether it is obtuse or not. It is known that a triangle can be formed with probability 1/4. An obtuse triangle can be formed with probability . If a triangle can be formed, it is obtuse with probability .

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

Snapshot 1: Only one-quarter of the experiments result in a triangle. This snapshot shows a typical example where a triangle cannot be formed: one of the three parts is longer than the sum of the lengths of the other two parts.
Snapshot 2: Here is another example where a triangle cannot be formed.
Snapshot 3: If a triangle can be formed, it is obtuse with quite a high probability (0.682).
Snapshot 4: Approximately one-third of the cases where a triangle can be formed are such that the triangle is not obtuse.
The probability that the random triangle is obtuse is calculated in [1]. The problem is also considered in [2, pp. 31–32].
In another Demonstration, we consider the related problem of generating random triangles in a rectangle; see the Related Links.
References
[1] M. G. C. Holterman, "Solution of Problem 858: Probability of an Obtuse Triangle," Mathematics Magazine, 46(5), 1973 pp. 294–295.
[2] P. J. Nahin, Digital Dice: Computational Solutions to Practical Probability Problems, Princeton, NJ: Princeton University Press, 2008.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+