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Feb
23
answered Show that $\sum_{n=1}^\infty nx^{n-1}$ converges uniformly on $[0,\frac{9}{10}]$
Feb
23
comment duality theory question
In your first equation, $x^T x = ||x||^2$ the norm of the vector. So you ask for the point of minimum norm across a certain affine subspace. Then you can generalize the point-to-line distance formula.
Feb
23
answered Proving $\frac{n^n}{e^{n-1}}<n!<\frac{(n+1)^{n+1}}{e^{n}}$ by induction for all $n> 2$.
Feb
21
comment Why is the Derangement Probability so Close to $\frac{1}{e}$?
doesn't it seem odd the error is less than $\frac{1}{(n+1)!} $ but $S_n$ has only $n!$ elements?
Feb
21
answered Why is the Derangement Probability so Close to $\frac{1}{e}$?
Feb
16
answered Derivation of the Boltzmann factor in statistical mechanics
Feb
15
revised Finding a value from 5 systems of equations of 5 variables(CHMMC 2014)
fixed +/- errors and fixed variable names
Feb
15
answered Finding a value from 5 systems of equations of 5 variables(CHMMC 2014)
Feb
12
comment For what values of $x$ will $ax^2+b$ be perfect squares?
solve in integers: $ax^2 - y^2 = b$ math.stackexchange.com/questions/8684/…
Feb
11
comment Variants of the change-of-variables formula
amazon.com/Geometric-Integration-Theory-Dover-Mathematics/dp/…
Feb
8
comment Minimal circle containing set of points
@brick it's unique because otherwise you can build a circle containing all the points, smaller than your original two "minimum" circles.
Feb
8
revised Minimal circle containing set of points
added 501 characters in body
Feb
8
revised Minimal circle containing set of points
found an important graphic
Feb
8
comment Minimal circle containing set of points
@brick the convex hull is a more delicate object than a circle, which is why I tried to do without it. My original two-line proof still works. The rest of the discussion is trying to construct the new minimizing circle $C_1$.
Feb
8
revised Minimal circle containing set of points
discussion of convex hulls
Feb
8
comment Minimal circle containing set of points
@brick You are correct, e.g. take $\{ 0, 1 \} \subset \mathbb{C}$ and adjoin the point $p = i$ in the complex plane. The minimal circles cut each other. We can still do induction where $C_1$ must surround $p$ and the convex hull of $x_1, \dots, x_n$.
Feb
8
revised Minimal circle containing set of points
relate to the problem of appolonius
Feb
8
answered Minimal circle containing set of points
Feb
6
comment Proving that $\int_{\mathbb{R}} f \ d\mu = \frac{1}{N}\sum_{i=1}^N f(\lambda_i)$
@Integral this seems like making a simple question really complicated. can't you define direc measure this way? $$ \int_{\mathbb{R}} f \ d\mu = \frac{1}{N}\sum_{i=1}^N f(\lambda_i)$$
Feb
5
revised Are there any differences between tensors and multidimensional arrays?
added 741 characters in body