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visits member for 3 years, 8 months
seen Jun 10 at 5:25

Jul
2
awarded  Curious
Jan
15
comment Pedagogy: How to cure students of the “law of universal linearity”?
@KCd Not to mention how they consider the problem "insignificant", using "kilowatt per hour" instead of "kilowatt-hour", "Amperes per hour" instead of "Ampere-hour" etc.
Jan
10
comment Pedagogy: How to cure students of the “law of universal linearity”?
Students? You mean people aged 16 and over? Here in Russia pupils in schools are got rid of such a math heresy in 5th-6th grades. Good old stick and carrot method: you have to prove each equality sign you write, or get downscored.
Dec
28
comment Ways to partition a sphere?
For game development purposes, there is a known approach to start from a certain hexagon/pentagon partition then partition it further by subdividing these tiles into smaller hexagons/pentagons recursively.
Nov
20
awarded  Popular Question
Sep
19
accepted Problem: Optimally distribute a fixed amount of work among a set of workers of different performance
Sep
19
comment Problem: Optimally distribute a fixed amount of work among a set of workers of different performance
So, the idea is that all the workers must finish at the same time. Otherwise, at any given time work that is performed by busy workers could have been distributed between currenty idle workers, reducing the finish (minimax) time. Sounds legit.
Sep
18
comment Let $f(z) = \frac{2z-1}{3z+2}$. Prove that $ \lim_{h \to 0}\frac{f(z_0+h)-f(z_0)}{h} = \frac{7}{(3z_0+2)^2}$
Don, if you allow using the arithmetics of limits, you could just have used it in the first place, substituting $h=0$ into limit expression due to the contunuity of it at $h=0$.
Sep
18
comment Let $f(z) = \frac{2z-1}{3z+2}$. Prove that $ \lim_{h \to 0}\frac{f(z_0+h)-f(z_0)}{h} = \frac{7}{(3z_0+2)^2}$
To prove that $A=\frac{7}{(3z_0+2)^2}$ is the limit of $B=\frac{f(z_0+h)-f(z_0)}{h}$ when $h \rightarrow 0$ you must show that for any $\epsilon > 0$ and $h_0: |h_0-0|<\epsilon$ the difference $|A-B(z_0,h_0)|$ can be majored by proper choice of $\delta > 0$: $|A-B|<\delta$. Rewrite the difference then try to pick a proper majorant $\delta$ functionally dependent on $\epsilon$ (and probably on $z_0$).
Sep
18
asked Problem: Optimally distribute a fixed amount of work among a set of workers of different performance
May
18
accepted If a 3D-cake is cut by $n$ planes yielding the maximum number of pieces, then what is the number of pieces with the cake crust?
May
18
comment If a 3D-cake is cut by $n$ planes yielding the maximum number of pieces, then what is the number of pieces with the cake crust?
I still don't understand. Consider we have 3 general circular divisions of the surface of the cake, having 8 pieces of crust. Next general cut would produce six new intersections with previous cuts on the cake surface, giving 14 pieces of crust. It corresponds to your formula, but how you project the cake surface on the plane? Riemann way? But would it transform cuts into circles? Or it is only important that the projections would be 'topological' circles?
May
17
comment If a 3D-cake is cut by $n$ planes yielding the maximum number of pieces, then what is the number of pieces with the cake crust?
@user14111: Corrected the heading
May
17
revised If a 3D-cake is cut by $n$ planes yielding the maximum number of pieces, then what is the number of pieces with the cake crust?
edited title
May
17
comment If a 3D-cake is cut by $n$ planes yielding the maximum number of pieces, then what is the number of pieces with the cake crust?
@user14111: The kind of such a cake is Kolobok: en.wikipedia.org/wiki/Kolobok
May
17
comment If a 3D-cake is cut by $n$ planes yielding the maximum number of pieces, then what is the number of pieces with the cake crust?
Consider a spherical cake is cut by two perpendicular planes. This produces four pieces of cake, all of them with crust. Two planes produce $n=2$ circles. Your formula gives number of crust-pieces equal to 2, but there are 4. Similarly, three planes give eight pieces, all of them with crust, but your formula gives 4.
May
17
asked If a 3D-cake is cut by $n$ planes yielding the maximum number of pieces, then what is the number of pieces with the cake crust?
May
17
comment Cutting a cube by plane cuts
@Amzoti: The OP seems to have abandoned his question, the answer, and the site.
May
17
comment Cutting a cube by plane cuts
@Amzoti It can be proved by induction. Consider having a cake already cut by $(n-1)$ planes. Add another, $n$-th cut. Inside the plane of that cut there are $(n-1)$ lines that produce number of regions defined by (Lazy Caterer's sequence)(n-1). Current cut plane produces that number of additional cake pieces ("above" or "below" the plane). Thus, $a(n)=a(n-1)+LCS(n-1)$.
May
15
revised Prove or disprove the following statements involving greatest common divisor
Edited the headline