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Jul
5
comment Looking for elementary proof of “for a circle, $C^2/A = 4 \pi$”
@ajotatxe: did you learn integration before you learned this result?
Jul
5
comment Looking for elementary proof of “for a circle, $C^2/A = 4 \pi$”
@MichaelHardy: I suppose that one can use either the area or the circumference of the unit circle as the basis for the definition of $\pi$. But then one would need to show that the same number of this definition reappears in the post's theorem's formula.
Jul
5
revised Looking for elementary proof of “for a circle, $C^2/A = 4 \pi$”
deleted 5 characters in body
Jul
5
asked Looking for elementary proof of “for a circle, $C^2/A = 4 \pi$”
May
28
revised What's the name of this tensor product?
deleted 18 characters in body
May
28
asked What's the name of this tensor product?
May
26
accepted Looking for a “Guide for the Perplexed by Low-dimensional Topology”
May
25
accepted Looking for student's guide to diagram chasing
May
25
comment Looking for a “Guide for the Perplexed by Low-dimensional Topology”
@GregoryGrant: At least part of the reason I find this stuff unsettling is that pretty much everywhere else (outside of areas devoted to these dimension-specific peculiarities) the sets $\mathbb{R}^n$ are treated as "basically the same" modulo a "trivial" difference in the dimensions. In particular, people routinely reason about "$\mathbb{R}^n$" (for some unspecified $n$) by analogy with their intuitions about $\mathbb{R}^d$ for $d \in \{1, 2, 3\}$. If every dimension has its own quirks, such thinking by analogy (where the target of the analogy is wholly unfamiliar) becomes highly suspect.
May
25
asked Looking for a “Guide for the Perplexed by Low-dimensional Topology”
May
23
awarded  Popular Question
May
19
revised On random rotational fluctuations in $\mathbb{R}^n$
removed a redundant term in second equation; fixed a couple of small typos
May
16
revised Conditions for “equal cardinality $\Rightarrow$ equal (finite) measure”?
deleted 3 characters in body
May
16
comment Conditions for “equal cardinality $\Rightarrow$ equal (finite) measure”?
@PhoemueX: I've edited my post in response to your comment.
May
16
revised Conditions for “equal cardinality $\Rightarrow$ equal (finite) measure”?
added 420 characters in body
May
16
revised Conditions for “equal cardinality $\Rightarrow$ equal (finite) measure”?
edited title
May
16
asked Conditions for “equal cardinality $\Rightarrow$ equal (finite) measure”?
May
14
awarded  Nice Question
May
12
comment On random rotational fluctuations in $\mathbb{R}^n$
Thanks for posting this! It is indeed beyond my grasp, as you predicted. Since it's probably bad form to accept an answer that one can't understand, I won't until I do, but I'm working on it! I will use your answer as something to aim for. Thanks again.
May
12
comment On random rotational fluctuations in $\mathbb{R}^n$
@StephenMontgomery-Smith: thanks, please post your answer; it will give me something concrete to aim for as I read on stochastic diff eqs (I started already).