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More triangles in circles


Best Answer BMAD, 30 March 2014 - 02:36 PM

Spoiler for I should have considered two fixed points

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#21 bonanova

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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.


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#22 bonanova

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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.


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#23 BMAD

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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.


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#24 bonanova

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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.


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#25 BMAD

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Posted 07 April 2014 - 05:49 PM

That is a mouthful  :(


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