## 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

# More triangles in circles

Spoiler for I should have considered two fixed points

Go to the full post

24 replies to this topic

### #21 bonanova

bonanova

bonanova

• Moderator
• 5918 posts
• Gender:Male
• Location:New York

Posted 04 April 2014 - 03:28 PM

Edit: It's actually more complicated than that hideous monstrosity... I left out that you would need to normalize the probabilities to sum to 1 instead of using raw squares of distances from the center.

You'd have the integrals you describe in the numerator of a fraction, divided  by the same integrals without the HasOrigin part in the denominator.

I think that would do the normalization. Ugh, agreed.

• -1
The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

### #22 bonanova

bonanova

bonanova

• Moderator
• 5918 posts
• Gender:Male
• Location:New York

Posted 07 April 2014 - 12:50 AM

Spoiler for Results for triangle

Correcting an error in the simulation program,

The probability that a random triangle inside an equilateral triangle covers its centroid is 0.24543 ...

The average size of a random triangle inside any triangle is 1/12.

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

Senior Member

• Members
• 1702 posts
• Gender:Female

Posted 07 April 2014 - 01:16 AM

Spoiler for Results for triangle

Correcting an error in the simulation program,

The probability that a random triangle inside an equilateral triangle covers its centroid is 0.24543 ...

The average size of a random triangle inside any triangle is 1/12.

I am assuming you mean the mean average.

• 0

### #24 bonanova

bonanova

bonanova

• Moderator
• 5918 posts
• Gender:Male
• Location:New York

Posted 07 April 2014 - 08:13 AM

The average size of a random triangle inside any triangle is 1/12.

I am assuming you mean the mean average.

The average area of random triangles drawn inside any triangle T is 1/12 the area of of T.

An affine transformation takes any given triangle into any other triangle while preserving relative (ratios of) areas.

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

Senior Member

• Members
• 1702 posts
• Gender:Female

Posted 07 April 2014 - 05:49 PM

That is a mouthful

• 0

#### 0 user(s) are reading this topic

0 members, 0 guests, 0 anonymous users