Jump to content


Welcome to BrainDen.com - Brain Teasers Forum

Welcome to BrainDen.com - Brain Teasers Forum. Like most online communities you must register to post in our community, but don't worry this is a simple free process. To be a part of BrainDen Forums you may create a new account or sign in if you already have an account.
As a member you could start new topics, reply to others, subscribe to topics/forums to get automatic updates, get your own profile and make new friends.

Of course, you can also enjoy our collection of amazing optical illusions and cool math games.

If you like our site, you may support us by simply clicking Google "+1" or Facebook "Like" buttons at the top.
If you have a website, we would appreciate a little link to BrainDen.

Thanks and enjoy the Den :-)
Guest Message by DevFuse
 

Photo
* * * * - 1 votes

Triangles inside circles


Best Answer bonanova, 25 March 2014 - 08:28 AM

Spoiler for Closing out a dormant topic

Go to the full post


  • Please log in to reply
5 replies to this topic

#1 bonanova

bonanova

    bonanova

  • Moderator
  • PipPipPipPip
  • 5652 posts
  • Gender:Male
  • Location:New York

Posted 28 February 2014 - 12:18 AM

A few puzzles posted in this forum have related to random triangles inside a circle.

 

By evaluating nasty integrals, or by my preferred method, simulation, it can be shown, perhaps surprisingly, that triangles constructed from sets of three uniformly chosen points within a circle cover only about 7.388% of the circle's area on average. After looking at Phil's recent problem on the subject, I simulated 1 million triangles to determine the median area. It turns out to be about 5.335% of the circle's area. Read: a random triangle has a 50% chance of being smaller.

 

If the distribution of random-triangle areas has a mean of about 7.4% and a median of about 5.3%, what value might you expect for the mode?


  • 0
The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#2 bonanova

bonanova

    bonanova

  • Moderator
  • PipPipPipPip
  • 5652 posts
  • Gender:Male
  • Location:New York

Posted 07 March 2014 - 03:07 PM

Spoiler for Hint


  • 0
The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#3 BMAD

BMAD

    Senior Member

  • Members
  • PipPipPipPip
  • 1664 posts
  • Gender:Female

Posted 14 March 2014 - 05:50 PM

Spoiler for guess

  • 0

#4 bonanova

bonanova

    bonanova

  • Moderator
  • PipPipPipPip
  • 5652 posts
  • Gender:Male
  • Location:New York

Posted 15 March 2014 - 02:05 PM

It's lower than that.


  • 0
The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#5 bonanova

bonanova

    bonanova

  • Moderator
  • PipPipPipPip
  • 5652 posts
  • Gender:Male
  • Location:New York

Posted 17 March 2014 - 12:30 AM

Spoiler for Big Hint


  • 0
The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#6 bonanova

bonanova

    bonanova

  • Moderator
  • PipPipPipPip
  • 5652 posts
  • Gender:Male
  • Location:New York

Posted 25 March 2014 - 08:28 AM   Best Answer

Spoiler for Closing out a dormant topic


  • 0
The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell




0 user(s) are reading this topic

0 members, 0 guests, 0 anonymous users