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 16 March 2014 - 06:13 AM

While our collective brain trust ponders the nature of triangles defined

by three uniformly random points chosen inside a circle, specifically

the mode of their areas, we ask another question.

Recalling that the mean and median areal coverage of its circle's area are

about 7.4% and 5.4%, what is the probability that a random triangle covers

its circle's center?

- Bertrand Russell

Posted 24 March 2014 - 04:14 PM

Spoiler for My first thoughts but I don't know where to go from here

Posted 24 March 2014 - 09:49 PM

Spoiler for My first thoughts but I don't know where to go from here

Sounds like an OK approach. You would need to do some (messy) integrals to account for the points being randomly chosen.

I like to think of this as more of a logic puzzle than a math exercise.

Is there a simpler way to think about the problem?

- Bertrand Russell

Posted 27 March 2014 - 05:55 AM

Spoiler for Hint

- Bertrand Russell

Posted 28 March 2014 - 03:11 PM

Spoiler for my weak thinking

I never get these right but ehh, why not try.

**Edited by BMAD, 28 March 2014 - 03:11 PM.**

Posted 28 March 2014 - 07:07 PM

Spoiler for Final clue

- Bertrand Russell

Posted 28 March 2014 - 08:02 PM

Spoiler for I came up with

**Edited by Rob_G, 28 March 2014 - 08:08 PM.**

Posted 30 March 2014 - 08:31 AM

Spoiler for I came up with

It's in that range. Can you nail it down? See my post #6.

- Bertrand Russell

Posted 30 March 2014 - 02:36 PM Best Answer

Spoiler for I should have considered two fixed points

**Edited by rookie1ja, 30 March 2014 - 08:50 PM.**

Posted 31 March 2014 - 09:15 PM

This answer is seen to apply for triangles covering the center of any containing shape that has four-fold rotational symmetry, including the circle, such as square and octagon.

Does to hold for triangles contained by other shapes, say a pentagon?

Does to hold for triangles contained by other shapes, say a pentagon?

- Bertrand Russell

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