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11h
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.
11h
comment Fast method to pick unique random numbers?
No, if for example cards 1 through 20 were already chosen, your method would have a much higher chance of picking 21 than any of the other remaining cards.
1d
comment Does Fractional Calculus have a real connection with Fractals? (or is it just an extra variable trick)
"Does Fractional Calculus have a real connection with Fractals (or is it just an extra variable trick)?" False dichotomy
1d
comment Parameterizing cliffs
Let $f(x)=\dfrac{1-x}{1-\alpha x}$ for $0<x<1$.
1d
comment Approximation of length of monotone curve
Isn't that the definition of the length of the curve?
2d
comment Approximation of length of monotone curve
Pick $n+1$ points on the curve, say $(x_0,f(x_0)), (x_1,f(x_1)), \ldots, (x_n,f(x_n))$ with $x_0=a$ and $x_n=b$. Connect them by line segments. For the line segment from $(x_i,f(x_i))$ to $(x_{i+1},f(x_{i+1}))$, draw a right triangle and observe that by the triangle inequality, the length of the line segment is not more than $|x_{i+1}-x_i| + |f(x_{i+1})-f(x_i)|$. The absolute values go away becuase $f$ is monotonic, and the sum over all $n$ line segments telescopes to $(b-a)+(f(b)-f(a))$.
2d
comment What is the name of convex polyhedra with congruent faces of regular polygons?
Apart from the cube and the dodecahedron, these would be the deltahedra I guess.
Apr
18
comment Fast method to pick unique random numbers?
The conceptually simplest way is to shuffle the deck and then take the first 45 cards. I like your method 1, which is basically a lazy version of that.
Apr
16
comment Why are these sums approximately equal?
What do you mean by "the mean value of $F$"?
Apr
16
comment How to construct a line with a given equal distance from 3 Points in 3 Dimensions?
The space of lines in 3D is four-dimensional. Each point-line distance constraint takes away one degree of freedom. So generically one should expect a one-dimensional family of solutions.
Apr
15
comment About the differentiability of $|x|$?
Regarding your last question: no, $|x|$ is continuous everywhere but its derivative does not exist at $0$.
Apr
15
comment About the differentiability of $|x|$?
Your derivation is not correct: $\sqrt{(x+h)^2}$ is not equal to $x+h$, it is $|x+h|$. The same goes for $\sqrt{x^2}$ (which you've mistyped as $\sqrt x$, by the way).
Apr
15
comment How to construct a line with a given equal distance from 3 Points in 3 Dimensions?
Equivalently, you are looking for the line(s) tangent to three spheres of radius $d$ centered at the three given points.
Apr
14
comment Does this have a name?
Try letting $A=\frac12(I-B)$ and proving that $B$ is orthogonal.
Apr
12
comment How can I minimize a quadratic on the unit simplex?
The definition given in Wikipedia is slightly incomplete. In quadratic programming one allows both linear inequality constraints, $Ax\le b$, and linear equality constraints, $Cx=d$. So the unit simplex can be defined as $-Ix\le0,e^Tx=1$.
Apr
12
comment How can I minimize a quadratic on the unit simplex?
This is known as quadratic programming. The Wikipedia page lists a number of solution methods.
Apr
10
comment Displaying images on Matlab.
You could use flipud inside your imshow call. // Unrelated: consider forcing all the 3D plots to have the same vertical scale.
Apr
10
awarded  Guru
Apr
10
awarded  geometry
Apr
6
comment Can anyony explain Why the $0^0\neq1$
What is WF? Wol Framalpha?