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Manitou
Ensign, Junior Grade
Joined: 17 Sep 2007
Posts: 43
Location: michigan, bob
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 Tue Mar 11, 2008 9:43 am I conclude |
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Believably 2/3 is one of the possible three answers in a book that I read for the first post concerning any random chord less then the radius. If any pt. on the circumference is connected to another random pt. on the circumference it will have 1/3 chance (considering the diameter) on either side for it's chord to be =< then the radius. 1/3 on either side is 1/3 of the circumference and the other 2/3 is > then the radius.
The third answer considers a random order of points evenly distributed throughout the circle. The inner Circle with (sq. rt. 3 divided by 2) as the radius has only mid-pts. for chords that are greater then the radius. The area of the inner circle in relation to the outer circle is the answer. This is (((sq rt 3 divided by 2) ^ 2) * pi) and is (3/4 * pi). the area of the unit circle being pi and the answer is 3/4.
The fourth answer is something I'm trying but I don't know the mathematics. Their is an inconsistency in the third answer. Mathematics says that on a planular surface there are an infinite and even distribution of pts. If their are an infinite # of lines passing through a circle and ambiguously larger than the circle one should consider angular possibilities for each of the mid-pts. Near (sq. rt. 3 / 2)R their can only be one possibe angle and near the circumference the angle could extend 1/3 on either side of the diameter. Also, needless to say, all mid-pts. in the inner circle would have a constant because all angles there would fit the criteria. If this is correct their would be a greater volume of small chords near the circumference.
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brianbrane
Freshman Cadet
Joined: 20 Dec 2006
Posts: 8
Location: here
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| Tue May 06, 2008 2:07 pm |
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| Oliver wrote: | | The correct answer to question 1 is indeed "2". |
You would have to pose the question differently for this to be the correct answer.
What integer do you end up with?
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Oliver
Thought Maker
Joined: 28 Feb 2004
Posts: 6096
Location: Antwerp, Belgium
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| Tue Sep 16, 2008 4:41 am |
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| brianbrane wrote: | | Oliver wrote: | | The correct answer to question 1 is indeed "2". |
You would have to pose the question differently for this to be the correct answer.
What integer do you end up with? |
That's not true. I asked for any number and the answer is indeed an integer but it could have been any other.
I'd like to start this quiz again actually. Who wants to join the quiz?
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calvin
Lieutenant, Junior Grade
Joined: 31 Jul 2008
Posts: 78
Location: SoCal
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| Tue Sep 16, 2008 3:44 pm |
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i'm game.
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Thomas
Pool Princess
Joined: 08 Jul 2001
Posts: 19730
Location: Manchester
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| Tue Sep 16, 2008 4:09 pm |
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Some of the questions are a bit beyond me, but I am about to start my second year of a mathematics degree, so I should be able to give some of the questions a go.
-------signature-------
Gloss rhymes with hair!
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Seven of Nine
Sammie's Mammy
Joined: 16 Jun 2001
Posts: 7871
Location: North East England
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| Thu Sep 18, 2008 2:07 am |
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If I feel comfortable with some of them (I'm just doing AS Level Maths, so not great yet  ) I'll give them a go.
May also give some to someone in my class 
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Oliver
Thought Maker
Joined: 28 Feb 2004
Posts: 6096
Location: Antwerp, Belgium
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| Fri Sep 19, 2008 4:47 am |
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Great! 3 people so far! I'll wait some more in order to get some more poeple going...
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lionhead
Rear Admiral
Joined: 26 May 2004
Posts: 4020
Location: The Delta Quadrant (or not...)
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| Fri Sep 19, 2008 8:09 am |
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No way i'm gonna miss out.
-------signature-------
Never explain comedy or satire or the ironic comment. Those who get it, get it. Those who don't, never will. -Michael Moore
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