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

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Guest Message by DevFuse

Started by bonanova, Feb 28 2014 12:18 AM

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

Spoiler for Closing out a dormant topic

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5 replies to this topic

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**?

- Bertrand Russell

Posted 07 March 2014 - 03:07 PM

Spoiler for Hint

- Bertrand Russell

Posted 14 March 2014 - 05:50 PM

Spoiler for guess

Posted 15 March 2014 - 02:05 PM

It's lower than that.

- Bertrand Russell

Posted 17 March 2014 - 12:30 AM

Spoiler for Big Hint

- Bertrand Russell

Posted 25 March 2014 - 08:28 AM Best Answer

Spoiler for Closing out a dormant topic

- Bertrand Russell

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