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I've often heard it said (most recently by xkcd in the comic-off with the New Yorker) that it is impossible to loop things through one another in dimensions. Assuming this is true, and that I understand the definition (that two objects are linked if they are not intersecting but cannot be rigidly translated and rotated to an arbitrary separation without intersecting), why doesn't this generalization of the torus work?
Admittedly, it tapers to 0 thickness near , but what's wrong with the fundamental idea of interlocking two of these so that shifting them in w can't free them because one gets too small? -- Tardis ( talk) 02:48, 20 October 2008 (UTC)
I think that the sentence it is impossible to loop things through one another in dimensions refers to special situations, most likely to objects that are immersed in dimensions, meaning that you can unlink them in the larger dimensional space (this has an immediate application in comix). Also, two closed curves (that is embeddings of S^1 ) in the dimensional space cannot be linked, as a simple transversality argument shows. Otherwise, in general, there are of course examples. -- PMajer ( talk) 07:07, 20 October 2008 (UTC)
Hello. What is the equation of the reciprocal function reflected upon y = 2x? I reflected the asymptotic lines (x and y axes) of upon the reflection line and sketched the new function. It looks like a hyperbola, which puzzles me after reading the article. Thanks in advance. -- Mayfare ( talk) 03:39, 20 October 2008 (UTC)
I forgot to mention that the equation is in the form of 12x2 + bxy + cy2 + d = 0; . Sorry. -- Mayfare ( talk) 01:31, 21 October 2008 (UTC)
Does 5+0=908235482947578679402? —Preceding unsigned comment added by Banna ant ( talk • contribs) 16:24, 20 October 2008 (UTC)
without meaning to start a debate, would you say excelling in maths would be associated with developing a certain type of personality? I mean that the same person, Joe, 17, is considering studying maths intensively and studying literature. If he does study maths, and excels, will he develop a certain type of personality concurrently? (On average, and versus the "control" of doing the other thing). Thanks! —Preceding unsigned comment added by 94.27.161.108 ( talk) 19:53, 20 October 2008 (UTC)
I think maths appeal to people who like a sense of the absolute in the universe. That there are answers that does not depend on the political environment.
122.107.147.49 (
talk) 08:53, 21 October 2008 (UTC)
My own experience from doing mathematics, rather that merely reading mathematics, is that it improved my ability to concentrate and my patience against other people. I think there is no such thing as an impatient and short-tempered mathematician. Bo Jacoby ( talk) 10:49, 21 October 2008 (UTC).
Mathematics desk | ||
---|---|---|
< October 19 | << Sep | October | Nov >> | October 21 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
I've often heard it said (most recently by xkcd in the comic-off with the New Yorker) that it is impossible to loop things through one another in dimensions. Assuming this is true, and that I understand the definition (that two objects are linked if they are not intersecting but cannot be rigidly translated and rotated to an arbitrary separation without intersecting), why doesn't this generalization of the torus work?
Admittedly, it tapers to 0 thickness near , but what's wrong with the fundamental idea of interlocking two of these so that shifting them in w can't free them because one gets too small? -- Tardis ( talk) 02:48, 20 October 2008 (UTC)
I think that the sentence it is impossible to loop things through one another in dimensions refers to special situations, most likely to objects that are immersed in dimensions, meaning that you can unlink them in the larger dimensional space (this has an immediate application in comix). Also, two closed curves (that is embeddings of S^1 ) in the dimensional space cannot be linked, as a simple transversality argument shows. Otherwise, in general, there are of course examples. -- PMajer ( talk) 07:07, 20 October 2008 (UTC)
Hello. What is the equation of the reciprocal function reflected upon y = 2x? I reflected the asymptotic lines (x and y axes) of upon the reflection line and sketched the new function. It looks like a hyperbola, which puzzles me after reading the article. Thanks in advance. -- Mayfare ( talk) 03:39, 20 October 2008 (UTC)
I forgot to mention that the equation is in the form of 12x2 + bxy + cy2 + d = 0; . Sorry. -- Mayfare ( talk) 01:31, 21 October 2008 (UTC)
Does 5+0=908235482947578679402? —Preceding unsigned comment added by Banna ant ( talk • contribs) 16:24, 20 October 2008 (UTC)
without meaning to start a debate, would you say excelling in maths would be associated with developing a certain type of personality? I mean that the same person, Joe, 17, is considering studying maths intensively and studying literature. If he does study maths, and excels, will he develop a certain type of personality concurrently? (On average, and versus the "control" of doing the other thing). Thanks! —Preceding unsigned comment added by 94.27.161.108 ( talk) 19:53, 20 October 2008 (UTC)
I think maths appeal to people who like a sense of the absolute in the universe. That there are answers that does not depend on the political environment.
122.107.147.49 (
talk) 08:53, 21 October 2008 (UTC)
My own experience from doing mathematics, rather that merely reading mathematics, is that it improved my ability to concentrate and my patience against other people. I think there is no such thing as an impatient and short-tempered mathematician. Bo Jacoby ( talk) 10:49, 21 October 2008 (UTC).