I hadn't meant to be accusatory -- obviously, the question is a natural one, and there is at least one Putnam problem which I can recall that is very similar. My point was simply to draw attention to the book, which is soon to come out is a second edition, which contains lots of very nice problems and solutions. Loren ----- Original Message ----- From: "Stephen B. Gray" <stevebg@roadrunner.com> To: "math-fun" <math-fun@mailman.xmission.com> Sent: Tuesday, August 31, 2010 5:03 PM Subject: Re: [math-fun] left vs. right
That's very curious. I thought the problem up myself as part of a larger inquiry, which I'm still working on. I'd buy the book but it costs $40 and I don't really have time for other problems.
Steve Gray
On 8/31/2010 7:22 AM, Loren and Liz Larson wrote:
This problem appears as Problem 67 in "The Wohascum County Problem Book", Gilbert, Krusemeyer, Larson, MAA, 1993.
----- Original Message ----- From: <rcs@xmission.com> To: <math-fun@mailman.xmission.com> Cc: <rcs@xmission.com> Sent: Monday, August 30, 2010 5:32 PM Subject: Re: [math-fun] left vs. right
Forwarded from SBG ...
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Date: Mon, 30 Aug 2010 12:08:08 -0700 Subject: Re: [math-fun] left vs. right From: "Stephen B. Gray" <stevebg@roadrunner.com>
Here's an exercise in 3D visualization. Given a point P, is it possible to construct FIVE rays coming out from P such that every ray makes an obtuse angle (>90 degrees) with every other one? (That's 10 angles that must be obtuse.) Explain your answer.
Steve Gray
On 8/30/2010 11:44 AM, James Buddenhagen wrote:
Interesting. I always assumed that people who had trouble with maps, cardinal directions, etc. were not math people. Perhaps it is because I was around maps since a child that I have always puzzled that some people have trouble with them. When heavy fog or overcast I get lost much easier than on clear sunny days, but I do not consciously think about the sun or shadows.
Whereas visualizing geometric solids seems easy for me, this I assume is learned. Nonetheless, I am almost always confused by illustrations of how to insert cards in ATM machines, and have even resorted to first trying the opposite of what I think it says, my wife never has this problem. Also, she finds ambiguous directions that others give about how to get somewhere unambiguous, while I am weighing the odds of what interpretation to give. I guess people are just different.
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