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

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Guest Message by DevFuse

Started by bonanova, Mar 16 2014 06:13 AM

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

Spoiler for I should have considered two fixed points

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24 replies to this topic

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.

- Bertrand Russell

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.

- Bertrand Russell

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.

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.

- Bertrand Russell

Posted 07 April 2014 - 05:49 PM

That is a mouthful

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