Re: [math-fun] left vs. right
Here's a possibly harder 3D visualization challenge: Draw a picture of a (topological) Moebius band in 3-space whose boundary is a perfect circle. (This can be done by continuously deforming the usual version.) --Dan -------------- Stephen wrote: << 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.
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On 8/30/2010 7:29 PM, Dan Asimov wrote:
Here's a possibly harder 3D visualization challenge:
Draw a picture of a (topological) Moebius band in 3-space whose boundary is a perfect circle. (This can be done by continuously deforming the usual version.)
--Dan
Try this: draw two interlocked equal circles that are "close together." They form the edges of a Moebius strip, so visualize the space between the circles filled with a flat band. I thought of that immediately but had to draw a crude representation to convince myself that it's correct. (Unless it isn't!) Steve Gray
That doesn't work. Remember, a Moebius band has a *single* edge, which can be deformed into a *single* circle. Not two. The original question asked by Dan correctly calls for a single circle. Your visualization works if you link the two circles, but then you're back to the original problem of deforming the result into a single circle. Tom Stephen B. Gray writes:
On 8/30/2010 7:29 PM, Dan Asimov wrote:
Here's a possibly harder 3D visualization challenge:
Draw a picture of a (topological) Moebius band in 3-space whose boundary is a perfect circle. (This can be done by continuously deforming the usual version.)
--Dan
Try this: draw two interlocked equal circles that are "close together." They form the edges of a Moebius strip, so visualize the space between the circles filled with a flat band. I thought of that immediately but had to draw a crude representation to convince myself that it's correct. (Unless it isn't!)
Steve Gray
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Tom is right. The thing I suggested seems to have a full twist instead of a half-twist. On 8/30/2010 8:36 PM, Tom Karzes wrote:
That doesn't work. Remember, a Moebius band has a *single* edge, which can be deformed into a *single* circle. Not two. The original question asked by Dan correctly calls for a single circle. Your visualization works if you link the two circles, but then you're back to the original problem of deforming the result into a single circle.
Tom
Stephen B. Gray writes:
On 8/30/2010 7:29 PM, Dan Asimov wrote:
Here's a possibly harder 3D visualization challenge:
Draw a picture of a (topological) Moebius band in 3-space whose boundary is a perfect circle. (This can be done by continuously deforming the usual version.)
--Dan
Try this: draw two interlocked equal circles that are "close together." They form the edges of a Moebius strip, so visualize the space between the circles filled with a flat band. I thought of that immediately but had to draw a crude representation to convince myself that it's correct. (Unless it isn't!)
Steve Gray
participants (3)
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Dan Asimov -
Stephen B. Gray -
Tom Karzes