cube

1. probability involving rubix cube

See the attachment. why is the probability of selecting orange side of perfectly solved rubix cube 1/5 ((1/6)/(1/ 5/6)) rather than 1/6 ?
2. Branch of the cube root

Let $f(z)=z^{1/3}$ be the branch of the cube root whose domain of definition is given by $0<\theta<2\pi$, $z\neq 0$ (i.e. the branch cut is along the ray $\theta=0$.) Find $f(-i)$. Could someone please help me understand the question? I'm not too clear on "branches" and "branch cuts".
3. Burnside's Lemma Application

Question: How many different colored cubes are there in which each face is colored either red or white or blue? I know we have to use Burnside's Lemma to solve this. (1/|G|)* Σ f(g) where f(g) are the number of fixed points of g. I also know that one of the trivial values will be 3^6, but...
4. Area of Cube Problem

So the question is as follows: The side of a cube has length x. Express (a) x as a function of the volume V of the cube, (b) the surface area S of the cube as a function of x, and (c) the volume V as a function of the surface S. For (a), I got x=\sqrt[3]{V} For (b), I got S=6x^2 The book...
5. Orthogonal Projections of Cube

I'm having trouble writing the area of the orthogonal projection of this cube onto the xy-axis as a function of the length of its orthogonal projection onto the z-axis for any length a. In a previous part of the question I had to prove that above area and length were always equal, and ended up...
6. Shortcut To Identify Cube Nets.

hi all.. i am frustrated, how to easy find & identify a cub nets.. like this : thanks a lot.... zidan3311
7. SAGE Rubiks Cube

I have been using SAGE to solve the 3x3x3 rubiks cube. Does anyone use SAGE for various recreational puzzles? I am looking to try something besides the rubiks cube
8. abc is cube

We have integers a,b,c \neq 0 where \frac{a}{b} + \frac{b}{c} + \frac{c}{a} is integer too. Prove that abc is a cube.
9. Can you manually compute cube root like you do square root?

Can you manually compute cube root like you do square root?
10. A Diagonal of a Cube

What is the angle made by a diagonal of a cube and a touching diagonal of a face of the cube?
11. Cube Root Index Division Q

So I've been doing indices all morning and along pops this question: Maybe my brain is hurting and I need a break, but how the fudge does this equal '2'?
12. Divide a cube

Could we divide a cube into 2014 smaller cubes? (small cubes not have to be identical...) I see this: Cube Dissection -- from Wolfram MathWorld And answer is: YES, but how to divide it into 2014 cubes? Thank you
13. Orders of elements for rotational symmetries of cube

I am having lots of trouble doing this problem because I have particularly poor visualization skills. (Or maybe haven't developed them well yet). I would appreciate any help on this math problem. Here is the question: Suppose a cube is oriented before you so that from your point of view...
14. 4 dimensional cube properties

lets construct a 4D cube, it has 2^4=16 corners and 2*4=8 3D faces and 24 2 dimensional faces. the 8 3D faces contribute 4 edges and the total edges is 8*4=32. so can you know these properties by deduction or visualization somehow? maybe there is an Euler characteristic? anyway I guess...
15. Hilbert Cube Homeomorphism

I have JUST been introduced to the Hilbert Space (\ell^2 space), and I have to show the following: Prove that ([-1,1]^{\infty},\Omega_p) is homeomorphic to the Hilbert Cube. \Omega_p is the product topology and the Hilbert Cube is a subspace of the Hilbert Space where each term of the...
16. Cube

A cube of side length 2 centimeters is rotated 360 degrees about the line connecting the centers of two opposite faces of the cube. What is the volume of space, in cubic centimeters, that is swept by this revolution? I am not sure about this problem. Would you please give hints or guides to...
17. How many 3d coordinates are needed to compute a parallelepiped or cube?

I am working on a project that requires deriving from a single 3d coordinate (x,y,z) a 3d space having a random shape of a geometrical figure e.g. a cube-like figure. The idea is to build a 3d geometrical figure that will contain the single 3d coordinate. For example, one way is to derive from...
18. flux helps for cube

Hello,I would really appreciate guidance with this .THanks. Do I find ∫∫F.nds for each face? or ?... Given that F=(x-y²)i+yzj+x²zk calculate the flux of F out of the cube with vertices at (0,0,0),(1,0,0),(1,1,0),(0,1,0),(0,1,1),(1,1,1),(1,0,1) and (0,0,1).
19. Cube root of complex number pls help

If (x+iy)^3=8i,prove that x((x^2)-3(y^2))=y((y^2)-3(x^2))=2,show that these equations have one solution in which x=y.And hence find one of the cube root of 2-2i.Find the quadratic equation satisfied by the other cube roots of 2-2i ans -i-i;z^2-(i+i)z+2i=0;0.5(1+sqrt 3)+0.5(1-sqrt...
20. complex nos finding cube root

If (x+iy)^2=8i,prove that x((x^2)-3(y^2))=y((y^2)-3(x^2))=2,show that these equations have one solution in which x=y.And hence find one of the cube root of 2-2i.Find the quadratic equation satisfied by the other cube roots of 2-2i ans -i-i;z^2-(i+i)z+2i=0;0.5(1+sqrt 3)+0.5(1-sqrt...