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Jan
16
comment Is $G^{(X, Y)} = (G^X)^Y?$ ($A^B$ just means that $B$ is mapped to $A$)
I think you're misunderstanding either what the notation $A^B$ means or what it means to map a codomain to a domain. Nevertheless, it is true that $G^{X\times Y}=(G^X)^Y$, this is called currying.
Jan
15
comment Functions Mapping Integers to Zero?
@David: That gives no greater generality because any $f(x)=h(x)g(x)$ obtained through your procedure can also be obtained as $\sin(\pi x)\left(\frac{h(x)}{\sin(\pi x)}g(x)\right)$ in Théophile's procedure.
Jan
15
comment What is the point of finding a limit? Does limit give us a real/exact value?
Alternatively, there is only one line passing through $(a, a^2)$ such that the parabola is entirely on one side of the line.
Jan
13
comment How to find the corners of a shape given 4 inequalities?
Considering every possible pair of inequalities gives you $\binom42 = 6$ candidate vertices. Discard the ones that do not satisfy the other two inequalities.
Jan
13
comment How does $(1+\sin x)\cos x =\cos x+\sin x \cos x$? I have a feeling i missed a basic fact
$(a+b)c=ac+bc$, y'know?
Jan
13
comment Function for this 3D curve
Try $x + y + z + a (x y + y z + z x) = 1$ for some $a>0$.
Jan
12
comment Generalizing the Cantor Set to the $n$-dimensional plane
See Cantor dust, and perhaps also Sierpinski carpet.
Jan
12
comment Cis Graphs (Finding Values)
The key idea is that $\operatorname{cis}x=\operatorname{cis}y$ if and only if $x$ and $y$ differ by an integer multiple of $2\pi$. Try proving that. (And yes, $2k\pi$ can be on either side of your equation.)
Jan
11
comment Determining isometric depth
Replace $(\text{width}+\text{height})/2$ with just $\text{height}$.
Jan
10
comment Would anybody be able to find the general formula for this pattern?
Sure looks like $M_{n-1} - M_{n-2} + M_{n-3} - M_{n-4} + \cdots$.
Jan
9
comment Add weights to inputs of x-value function to optimize regression
It is still very unclear what you are trying to achieve. Regression already gives the function that minimizes the total squared error with respect to the data.
Jan
9
comment Sequence of compactly supported functions approximating $x^2$
By switch gears I mean make $f''=2$ again so that when $f=0$ you also satisfy $f'=0$.
Jan
9
comment Sequence of compactly supported functions approximating $x^2$
On $-100\le x\le100$ you have $f''=2$. For $x>100$ have $f''$ decrease continuously to $-2$ and then stay there. Your function will eventually start decreasing towards $0$. At some larger $x$ you will have to switch gears again to make it meet the $x$-axis smoothly.
Jan
9
comment What is the shortest LOOP program that outputs 2016?
"Shortest program" questions generally go on codegolf.stackexchange.com, but this one has a sufficiently mathematical flavour that I think it fits better here.
Jan
8
comment What are some math concepts which were originally inspired by physics?
The dot product and cross product of vectors in $\mathbb R^3$ were invented by Heaviside and Gibbs to simplify Maxwell's equations of electrodynamics, which were originally expressed in terms of quaternions.
Jan
7
comment Is this (self intersecting) surface considered one sided?
@Alex That's true. Personally I was willing to believe (from the shape of the isoparametric contours) that $c(t)$ and $c'(t)$ were never parallel, and I was addressing the issue of self-intersections instead.
Jan
7
comment Is this (self intersecting) surface considered one sided?
@Alex Sorry if my terminology is sloppy; I'm not a topologist nor a differential geometer.
Jan
7
comment Is this (self intersecting) surface considered one sided?
@Alex If we treat the given surface as parameterized by $f:[0,1]\times[0,1]\to\mathbb R^3:(s,t)\mapsto sc(t)$ "glued" along $f(s,0)=f(s,1)$, where $c:[0,1]\to\mathbb R^3$ is the input closed curve, then we can define the normal at any point $(s,t)$ on the parameterization by normalizing the vector $c(t)\times c'(t)$. This normal vector field is "consistent" in that the normals point in the same direction on both sides of the gluing (unlike the Möbius strip, where the normals necessarily point in opposite directions).
Jan
7
comment Is this (self intersecting) surface considered one sided?
I think this still counts as a two-sided surface, because you can define a consistently oriented normal field. In fact because you are connecting a closed curve to a point, this is just an immersion of a disk into 3-space (with the center of the disk mapped to the origin and the circumference mapped to the curve).
Jan
7
revised Is this (self intersecting) surface considered one sided?
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