Reputation
22,758
Next tag badge:
84/100 score
19/20 answers
Badges
3 36 85
Newest
 Guru
Impact
~413k people reached

54m
comment Can a non-convex set be partitioned into a set of nearly convex subsets?
This will probably depend on the metric $d$. If you take the Hausdorff distance, you can always choose each $s_i$ to be contained in a ball $b_i$ of diameter $\epsilon$. Then $s_i$ is automatically within $\epsilon$ of the convex set $b_i$.
1h
comment curious about a made up paradox
@Dmitry: It means that there is only a one in $1.18\times10^{14}$ chance that you will ever get out of debt. Alternatively, if you have $1.18\times10^{14}$ gamblers all playing the game repeatedly forever, probably all but one of them will never ever get out of debt no matter how long they play.
3h
comment Is there an alternative encoding scheme to binary where similarity of pattern correlates with size of number?
"The reflected binary code, also known as Gray code after Frank Gray, is a binary numeral system where two successive values differ in only one bit (binary digit)."
2d
comment Why is $\sinh$ often pronounced “shine”?
Note that /t∫/ is the "ch" sound, as in China. So we have the pronunciations shine, cinch, sine H.
2d
comment Why is $\sinh$ often pronounced “shine”?
You can say the word "hyperbolic" in 1/10th of a second? That might cause more confusion than it eliminates!
2d
comment What is the point of basis vectors?
Suppose I give you an arbitrary plane in 3D Euclidean space passing through the origin. It is a 2-dimensional vector space. How would you denote a point on it as $(x_1,x_2)$? See also this MathOverflow question: Vector spaces without natural bases.
2d
comment Card layouts and graph theory
Not according to MathWorld or Wikipedia. $u\to v$ and $v\to u$ are two different edges, not multiple copies of the same edge.
2d
comment Card layouts and graph theory
Pretty sure you can't have both edges $u\to v$ and $v\to u$ using planar convex cards.
2d
comment Proof of Hunt's Interpolation
Typographical suggestion: use \langle $\langle$ and \rangle $\rangle$ for angle brackets and \| $\|$ for double bars.
2d
comment Help sketching 'Jungle River Metric' in $\mathbb{R}^2$
I see, this is the metric for a fish swimming in a river flowing along the $x$-axis which has infinitely many tributaries parallel to the $y$-axis.
Apr
23
comment What does a separation in lines mean?
It makes about as much difference as putting a line break between two English sentences.
Apr
22
comment Is this simplification 'allowed'?
Yes, $p/q=0$ if and only if $p=0$ and $q\ne0$.
Apr
22
comment Why aren't natural numbers inherently present in the universe?
How exactly does a observer "observe" $\pi$ in a way that does not extend to "observing" $1$?
Apr
22
comment Generalizing convexity of sets
@Igor: No, two points in the middle of opposite edges would require three segments. A triangular ring would work though!
Apr
22
comment Generalizing convexity of sets
@Igor: No, a star-convex set is 2-convex but is not necessarily the union of 2 convex sets.
Apr
22
comment Generalizing convexity of sets
Interesting question. Do you have an example of a 2-convex set that is not star-convex?
Apr
22
comment How can we prove that a three legged chair will never be wobbly?
The key fact is indeed that three points determine a plane, but connecting that to the stability of chairs requires a bit of elaboration that I don't have time for right now. Interestingly, a four-legged chair can be stable -- if one of the legs is sufficiently short and lies entirely inside the triangle formed by the other three.
Apr
22
comment What does a polynomial look like under projection of underlying space?
What makes you so sure that the projected function is still a polynomial? Try going through the formula Greg Martin linked to.
Apr
22
comment Method for determining the average deviation of data values over time?
Well, you could get the trend via local regression and compare each data point to that. But I'm not a statistician.
Apr
21
comment Find out the optimization type
You need to say something more about $f_1$ and $f_2$. If they are completely arbitrary then you can't guarantee anything. For example you could have $f_1(x)=f_2(x)=-1$ only when $x=(42,10^6)$ and $0$ everywhere else, in which case just evaluating $f_1$ and $f_2$ at other points gives you no information about the location of the minimum.