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Jul
25
comment prove $\sum\limits_{cyc} \frac {a^3} {b+c+d} \geq \frac {1} {3}$
For your idea, just add up all inequalities of type $a^2+b^2 \geq 2ab$.
Jul
25
comment prove $\sum\limits_{cyc} \frac {a^3} {b+c+d} \geq \frac {1} {3}$
@Macavity You're right. $f$ is not convex. Your second comment seems to work.
Jul
23
comment Graph containing every trees of size $n$ as subgraphs
Thanks for this interesting conjecture. But what I'm asking is the minimum number of edges required for some graph, while the conjecture is asking for all graph.
Dec
29
comment Dividing a deck of cards using only imagination
@hunter Let the two players be A and B and two cards be 1 and 2. A simply choose her card uniformly from 1 and 2, and pass the other to B. Now the cards are distributed uniformly, and since each individual knows his card, knowing the opponent's card does not add to that information.
Jun
13
comment Mathematical (or physical) formulation of life
Thanks for the recommendation! I will check that book too.
Jun
12
comment Mathematical (or physical) formulation of life
@DejanGovc I knew the title, but didn't know of its content! Thanks for pointing me out the book.
Jun
12
comment Mathematical (or physical) formulation of life
@SimonMarkett However I think it is not easy to describe how the life is emerged with the game of life. The patterns are designed carefully, and it seems hard to make them spontaneously from some initial state.
Jun
12
comment Mathematical (or physical) formulation of life
@SimonMarkett Yes, I heard of it before. I think the game of life partially answers the question. It has simple rules and various patterns emerging from the rules, some even reproducing another patterns!
Jun
12
comment Mathematical (or physical) formulation of life
Should I delete this question or change this to a community wiki? I'm new to this site so any corrections are welcome.
Sep
20
comment Project Euler Problem 338
Sorry if it's not much related to the question. But I'm curious if we could prove that dividing into two staircases is the only way of forming another rectangle. How can we do this?
Sep
20
comment What is the smallest number of $45^\circ-60^\circ-75^\circ$ triangles that a square can be divided into?
@Peter I think 45-60-75 means that the triangle has 45, 60, 75 as its angles (in degree).
Sep
15
comment What is the smallest number of $45^\circ-60^\circ-75^\circ$ triangles that a square can be divided into?
@Ed Pegg How did Laczkovich packed the square with triangles? I'm very curious :D
Sep
11
comment Integer solutions to $(a_1+a_2+\cdots+a_n)^n=a_1a_2\cdots a_n$?
$(a_1+...+a_n)^n \geq (a_1)(a_2)\cdots(a_n)=a_1\cdot \cdots \cdot a_n $ The equality only holds iff $a_1 = \cdots = a_n = 0$
Aug
25
comment Does a 'universal' group/ring/field/topology/etc. exist?
@Miha Yes. If anything makes you incomprehensible feel free to modify my question to make it easier to understand.
Aug
25
comment Does a 'universal' group/ring/field/topology/etc. exist?
@Ilmari Karonen Thanks for grammar correction! I'm still a novice in English so it helps me a lot.
Aug
23
comment A separable locally compact metric space is compact iff all of its homeomorphic metric spaces are bounded
Thanks for all who considered my question!
Aug
21
comment A separable locally compact metric space is compact iff all of its homeomorphic metric spaces are bounded
He and I only took elementary topology, so the claim might become very trivial when one goes into deeper mathematics. If it is so, please tell us which theory can be employed. Thanks!
Aug
19
comment Prove convexity/concavity of a complicated function
Is $f$ the function you wanted to optimize in your previous question? :D Edit: Oh no I didn't realized that $f$ is one-variable here!
Aug
17
comment How to prove that this sequence converges? ($a_n=a_{a_{n-1}}+a_{n-a_{n-1}}$)
I think the sequence is Hofstadter-Conway $10000 Sequence! mathworld.wolfram.com/…
Aug
11
comment Let a; b; c and d be non-negative numbers such that a+b+c+d = 4. Prove that 4/(abcd) ≥ a/b + b/c + c/d + d/a
Brilliant! This solution covers the equality case (a, b, c, d) = (2, 0, 1, 1)! I thought only using dirty techniques would give that.