Timeline for Is there a unit for expression of degree how much space is curved?
Current License: CC BY-SA 3.0
10 events
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| Aug 19, 2016 at 17:35 | comment | added | Zo the Relativist | @count_to_10: yes, that is absolutely right. The mathematically precise way of saying that is that, in some local neighborhood of a point, the manifold can be approximated by the tangent plane to that point. | |
| Aug 19, 2016 at 15:35 | history | edited | user108787 | CC BY-SA 3.0 |
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| Aug 19, 2016 at 15:31 | comment | added | user108787 | @JerrySchirmer I will incorporate your comment in my answer. At my knowledge level, my immediate (and admittably newbie) response is to say this corresponds to the notion that at a "small" enough local level, $g_{\upsilon\nu}$ goes to $\eta_{\upsilon\nu}$ | |
| Aug 19, 2016 at 15:08 | comment | added | Zo the Relativist | I'd argue that Riemann curvature definitely has a unit -- inverse length squared. Note that the deviation of triangles from 180 degrees depends on the size of the triangle. | |
| Aug 16, 2016 at 17:53 | history | edited | user108787 | CC BY-SA 3.0 |
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| Aug 16, 2016 at 17:22 | comment | added | user108787 | @BenCrowell thanks Ben, I self study, so in answering the questions, it's as much for myself. TBH, it's the appropriate level for me as well. I will edit the post with your suggestion, as soon as I learn it myself :) | |
| Aug 16, 2016 at 17:15 | comment | added | user4552 | +1, nice conceptual answer at the appropriate level for the OP. This answer could be improved by explaining in the original example (the spherical triangle) that the Gaussian curvature is defined not as the angular deficit but as the ratio of the angular deficit to the area of the triangle. | |
| Aug 16, 2016 at 12:17 | vote | accept | dllhell | ||
| Aug 16, 2016 at 12:14 | history | edited | user108787 | CC BY-SA 3.0 |
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| Aug 16, 2016 at 12:07 | history | answered | user108787 | CC BY-SA 3.0 |