Reputation
15,117
Top tag
Next privilege 20,000 Rep.
Access 'trusted user' tools
Badges
3 13 39
Impact
~124k people reached

9h
comment Ricci curvature of the Grassmannian?
@Joe: As with your question about the diameter, the answer depends on a choice of metric, including overall scaling. (As Jason DeVito notes, the Grassmannian admits a unique homogeneous Kähler metric, which is necessarily Einstein with positive Ricci curvature. The value of the Einstein constant, or of the scalar curvature, depends on the scaling.)
16h
answered Gaussian curvature distribution: embeddable?
17h
reviewed Edit Sketching the image of a circle under a complex polynomial
17h
revised Sketching the image of a circle under a complex polynomial
grammar and format edit
17h
awarded  Sportsmanship
18h
answered Winding maps of spheres?
20h
comment whether any shape can be placed on a tiled surface?
Thank you for the clarification. :)
20h
comment Can someone illustrate the definition of manifold with a simple example?
Suffice it to say that every subset of $\Reals^{n}$ is Hausdorff and second-countable. :) Those properties are part of the "intrinsic" definition of a manifold mentioned just above the theorem, and make sense (only) in the axiomatic definition of a topological space. If you feel adventurous: Hausdorff and second-countable spaces. (To quote Morris Hirsch: "In a Hausdorff space, any two points can be housed orff [sic] from each other."
1d
comment Determining what set of points a curve can be expressed as a singlevariable-function
There are two related questions, and it's not entirely clear to me which you're asking: 1. Find the set of $x$ such that if $(x, y_{1})$ and $(x, y_{2})$ are on your curve, then $y_{1} = y_{2}$. 2. Find the set of $(x, y)$ on the curve such that _in some open neighborhood $V$_ of $(x, y)$, the intersection of $V$ with your curve may be expressed as the graph of a function $y = \phi(x)$. Interpretation 2. seems likelier; the implicit function theorem (checking that the partial with respect to $y$ is non-zero) gives a sufficient condition. Was the exact wording everything before "I guess..."?
1d
revised On an informal explanation of the tangent space to a manifold
Added discussion on coordinate vector fields per OP's clarifying comment.
1d
answered On an informal explanation of the tangent space to a manifold
1d
answered Homeomorphism between the set of invertible matrices and itself
1d
revised Do limsup and liminf exist only for oscillating sequences?
Added image to question body
1d
comment whether any shape can be placed on a tiled surface?
Then could you please clarify your question: Are you asking "What is the largest-area region that does not touch a vertex?"; "Is there a $C > 1$ such that every region of area at most $C$ can be rotated and translated so it does not touch a vertex?"; or something else?
1d
answered Can someone illustrate the definition of manifold with a simple example?
1d
comment Troubles understanding task for complex logarithm.
Could you please say something about how you think of the complex logarithm? Particularly: How was it defined? Do you know any of its algebraic or geometric properties? Do you know its real and imaginary parts?
1d
comment whether any shape can be placed on a tiled surface?
Did you mean "$C < 1$"? If so, was the proof Eric Naslund gave in the linked question not enough? Or are you asking something different?
2d
revised A piecewise $C^1$ curve has Jordan measure zero.
Tweaked title and LaTeX
2d
answered A piecewise $C^1$ curve has Jordan measure zero.
2d
comment A piecewise $C^1$ curve has Jordan measure zero.
@Rab: A set $\Gamma$ has Jordan measure zero if $\Gamma$ can be covered by finitely many sets (such as closed disks) whose total area is smaller than an arbitrary prescribed amount. For instance, if you have $n$ disks of radius $L/n$ covering $\Gamma$, their total area is $n \cdot \pi(L/n)^{2} = \pi L^{2}/n$, and this can be made as small as you like. Are you having trouble with 1. or 2., and if so could you say something about what exactly you're unsure about?