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10h
comment How to find the largest disk in a square when there are points we must avoid?
I believe what you need to check are the circles centered at the vertices of a generalized Voronoi diagram, whose sites are the $n$ given points and the $4$ edges of the square.
10h
comment How to find the largest disk in a square when there are points we must avoid?
I think if you arrange the points so that they fill the square with a big circular bite taken out of it, you can have the points supporting the largest empty circle be arbitrarily far from the convex hull.
10h
comment How to find the largest disk in a square when there are points we must avoid?
Almost, but not quite. Consider the skinny triangle on the boundary at the bottom right of your figure. Suppose one edge of the square is close to and parallel to its long edge. The largest circle in this neighbourhood is tangent to the edge and the upper two points. One of those points does not lie on the convex hull, so the configuration is not of the forms you consider.
22h
comment Does color affect purchase decisions across items?
Why strike out the older text instead of simply deleting it? If you need it later it'll still be in the edit history, you know.
1d
comment area of a bounded region
$x^3+x^3+1$? That's an odd way to write $2x^3+1$; going by the earlier version maybe it should be $x^3+x+1$? In either case there isn't any bounded region between the graphs, so I expect that there is an error in the question.
1d
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 $b_i$.
1d
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.
1d
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)."
Apr
24
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.
Apr
24
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!
Apr
24
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.
Apr
24
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.
Apr
24
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.
Apr
24
comment Proof of Hunt's Interpolation
Typographical suggestion: use \langle $\langle$ and \rangle $\rangle$ for angle brackets and \| $\|$ for double bars.
Apr
24
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.