What is Cube: Definition and 609 Discussions

In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.
The cube is the only regular hexahedron and is one of the five Platonic solids. It has 6 faces, 12 edges, and 8 vertices.
The cube is also a square parallelepiped, an equilateral cuboid and a right rhombohedron. It is a regular square prism in three orientations, and a trigonal trapezohedron in four orientations.
The cube is dual to the octahedron. It has cubical or octahedral symmetry.
The cube is the only convex polyhedron whose faces are all squares.

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  1. E

    Defining Entropy on a Rubik's Cube: Insights and Implications

    I have been thinking about finding a way to define entropy on a rubik's cube. My idea is to use the number of cubies that are not in their solved position as the macrostate. This works well because there is exactly one way for all the cubies to be in the solved position so it has entropy of...
  2. Atlas3

    Sphere in Cube: Can it be Defined?

    Can it be defined a disfigured sphere to approximate a cube mathematically? 8 corners equilateral to some extent. Not exact.
  3. K

    MHB Find Min Polynomial of $\alpha$ Over $\mathbb{Q} | Solution Included

    I started by setting $\alpha= e^{2\pi i/3} + \sqrt[3]{2}.$ Then I obtained $f(x) = x^9 - 9x^6 - 27x^3 - 27$ has $\alpha$ as a root. How can I proceed to find the minimal polynomial of $\alpha$ over $\mathbb{Q},$ and identify its other roots?
  4. Emmanuel_Euler

    Finding a cube root of a number without using calculator .

    HI EVERYONE I was thinking if we could find a cube root without using a calculator. square root was easy to find without calculator,but cube root i have no idea to find it. any help?? for example(cube root of 3 or 2)
  5. S

    Find induced charge on conducting cube in uniform field

    Problem statement, equations, and work done: A perfectly conducting cube is placed in a uniform electric field in the x direction (see attached). Step1 : Use Gauss's law to determine the electric field inside the cube.##\phi_E = 2E(r)A = \frac{q}{\epsilon_0} →...
  6. I

    Finding the points of a cube given two points.

    Question: A cube ABCD, has been placed somewhere in space and is cut by the xy plane. The z-axis indicates the height of the cube. We know that A = <10,7,4> and C = <9,5,6>, find B, D, A', B', C', D' (Where A', B', C', D' are the points which intersect with the xy plane. B and D have the same Z...
  7. goonking

    Solving for Height of a Falling Cube Using Kinetic Energy

    Homework Statement Homework Equations 1/2 mv^2 = mgh The Attempt at a Solution first, a side question, if p = mv, can't we just place p into 1/2 mv^2 so it becomes 1/2 p^2? anyway, on to the question, at the point where the cube falls off, the Fnormal should just about equal 0, correct? is...
  8. S

    MHB How Do I Identify the Net of a Cube?

    hello everybody... i have problem, how to easy find & identify a net of the cube.. do you have a easy tricks/method to figure it out this problem? thanks..
  9. anemone

    MHB Prove (a²+b²+6)/(ab) is a perfect cube

    The numbers $a,\,b$ and $\dfrac{a^2+b^2+6}{ab}$ are positive integers. Prove that $\dfrac{a^2+b^2+6}{ab}$ is a perfect cube.
  10. A

    Potential anywhere inside a cube

    Homework Statement All six faces of a cube, of side length ##L##, are maintained at constant, but different potentials. The left and right faces are at ##V_1## each. The top and bottom are at ##V_2## each. The front and back are at ##V_3##. Determine the electrostatic potential ##\Phi(x,y,z)##...
  11. 1

    Calculating the Period of SHM for a Suspended Cubical Box

    Homework Statement We have a cubical hollow box, edge length ##a## suspended horizontally from a frictionless hinge along one of its edges. The box is displaced slightly and undergoes SHM. Show that the period of the oscillation is given by ## T = 2\pi \sqrt{\frac{7\sqrt{2}a}{9g}} ## Homework...
  12. S

    Is Biot-Savart inverse cube or inverse square law?

    I know we can represent it two different ways. First: \mathbf{B} = \frac{\mu_0}{4\pi}\int_C \frac{I d\mathbf{l} \times \mathbf{\hat r}}{|\mathbf{r}|^2} If we open up unit vector, then it becomes: \mathbf{B} = \frac{\mu_0}{4\pi} \int_C \frac{I d\mathbf{l} \times \mathbf{r}}{|\mathbf{r}|^3} I...
  13. K

    Man pulling a cube on a rough surface

    Homework Statement A man of mass 70[kg] pules a box at an angle 100. the static coefficient of friction between his legs and the floor is 0.6 and the kinetic coefficient between the box and the floor is 0.3 What's the maximum's box's mass Homework Equations Friction: f=μN The Attempt at a...
  14. V

    Calculating Electric Field Flux for Non-Uniform Fields: Gaussian Cubes Example

    Homework Statement 6 Gaussian cubes are shown below. The surfaces are located within space containing non-uniform electric fields. The electric fields are produced by charge distributions located outside the cubes (no charges in the cubes). Given for each case is the side length for the cube...
  15. G

    Electric potential of a cube of 8 point charges

    Homework Statement Find the Electrostatic potential energy of a cubical configuration of point charges. (One charge on each corner of a cube). Each of the charges is 3.00e and the edge of the cube is 3 cm. Homework Equations U = kqQ/r The Attempt at a Solution I'm pretty sure I understand...
  16. Ahmed Abdullah

    Rubik's cube group element with the smallest order

    Wikipedia says that largest order of any element of Rubik's cube group is 1260 [PLAIN]http://upload.wikimedia.org/math/e/1/c/e1cff178a2562422492a4140a38f93ff.png. http://en.wikipedia.org/wiki/Rubik%27s_Cube_group What about element of smallest order (except the identity element)? I'll...
  17. K

    Size of a cube for a molecule of ideal gas

    Homework Statement The temperature of an ideal gas is 00C and the pressure is 1[atm]. imagine every molecule is enclosed in a cube, what's it's side length? Homework Equations PV=nRT Avogadro's number: 6.023E23 The Attempt at a Solution I assume volume of i liter: $$1[atm]\cdot...
  18. D

    MHB How to Calculate Cube Root of a Number in 10 Seconds

    The first and the most important step is to memorize the cubes of 1 to 9. These would form an important part of your toolkit in solving the cube roots. Here is a table for your convenience. 1 –> 1 2 –> 8 3 –> 27 4 –> 64 5 –> 125 6 –> 216 7 –> 343 8 –> 512 9 –> 729 Once you memorize this list...
  19. AdityaDev

    Life on a Cubical Earth: Imagining Gravity and Everyday Challenges

    I was thinking about a situation where we lived in a cubical earth! (Gravity is such that people at each surface will still feel that they are standing upright). I came up with some interesting situations like when a ship crosses an edge or throwing a ball from the edge of surface... What would...
  20. Ritzycat

    How Far Will the Ice Cube Travel Up the Slope?

    Question statement A 55g ice cube can slide without friction up and down a 25∘slope. The ice cube is pressed against a spring at the bottom of the slope, compressing the spring 10cm . The spring constant is 25N/m. When the ice cube is released, what distance will it travel up the slope before...
  21. Hijaz Aslam

    Gauss Law of Cube in non-uniform linear Electric Field.

    Gauss's Law states that if a Gaussian Surface encloses a charge ##q_{enc}## then the electric flux through the Gaussian Surface is given by ##\phi=q_{enc}/\varepsilon_{o}## . It also states that any external field does not contribute to the Electric Flux through the Gaussian Surface. I am bit...
  22. K

    Confusion about bound surface current of a cube

    If the magnetization vector is in the z direction, is the bound surface current of a cube always 0, since z cross z is 0, and x and -x cancels and y and -y cancels out?
  23. S

    Can a Steel Piping Cubic Bedframe Support Heavy Weight?

    Hi, so I'm currently trying to build a cubic bedframe out of metal pipes. The frame would essentially be a 7'x7'x5' rectangular prism (HxWxL, I.E. 7x5 being the base of it), with four 1' legs holding it up. However, I would like the top of the frame (The 7x5 square above the bed) to be able to...
  24. N

    Cube sliding down with frictionless slide

    Homework Statement A cube with m mass is released from the top of a slide, of h height, with a horizontal distance of d. [/B] Homework Equations Assuming there is no friction between the cube and the slide, ¿what is the minimal information i need to calculate the speed of the cube at the end...
  25. M

    Cube Projectile Motion: Air Resistance & Cross Sectional Area

    We have a solid cube with some mass that we fire as a projectile at some angle. The cube is launched in such a way that two of the faces are perpendicular to the initial velocity vector. Assuming there is air resistance, would the cube change its orientation while it flies, even if the mass is...
  26. C

    Strange behavior for orbits of inverse cube forces and higher?

    After working a homework assignment which required sketching effective potential energy for the gravitational/coloumb forces, I went and looked at a few effective potentials for inverse cube and inverse quartic (not sure if this is the right word; 1/r^4 force) forces, with inverse square and...
  27. snoopies622

    Expanding Cube Roots: Solving Limits with Maclaurin Series

    A quiz at the end of Steven Krantz's Calculus Demystified includes the following problem: Find \lim_{x \to \infty} [ \sqrt[3]{x+1} - \sqrt[3]{x} ] I see how one can use the Maclaurin series to get \sqrt[3]{x+1} = 1 + \frac {x}{3} - \frac {x^2}{9} + \frac {5 x^3}{81} + . . . but trying it...
  28. A

    Calculating Flux on a Rubik's Cube with a Point Charge at the Center

    Each sub-cube of the puzzle has edges 3.0 cm in length. A 8.0 nC point charge lies at the puzzle's center. What is the flux through the one face of the sub-cube labeled with the logo? Note: Its referring to a Rubik's Cube that has 8 sub cubes I used the equation where i divided the charge by...
  29. R

    MHB Are rationals adjoin cube root of 3 a field?

    Is \mathbb{Q}(\sqrt[3]{3})=\{a+b\sqrt[3]{3}+c\sqrt[3]{9}\mid a,b,c\in\mathbb{Q}\} a ring? If it is a ring, is it a field? I have shown that it is a ring; however, I am not sure that it is a field, since in my calculations it does not seem to be closed under inverses. But I read somewhere that...
  30. T

    MHB Given a quadratic in x, find the cube of x

    if $x^2 = x+3$ then $x^3 = ??$ Not sure about this would appreciate some help
  31. F

    Overall Force Acting on a Submerged Cube (in water)

    This is not homework or coursework. I have an exam coming up and this question is from a past paper and I am unsure why but it is confusing me a bit. Homework Statement A cube of side 0.3m which has an average density of 4500 kg/m^3 . Determine the overall force acting on the cube when it...
  32. F

    Entropy change of melting ice cube initially at -5°C

    Homework Statement Calculate the entropy change of an ice cube of mass 10g, at an initial temperature of -5°C, when it completely melts. cice = 2.1 kJkg-1K-1 Lice-water = 3.34x105 Jkg-1 Homework Equations dQ = mcdT dS = \frac{dQ}{T} ΔS = \frac{Q}{T} Q = mL The Attempt at a...
  33. M

    Calculate Mass of Ice Cube from Calorimetry Experiment

    A cube of ice is taken from the freezer at -8.5C and placed in a 95g aluminium calorimeter filled with 310g of water st room temperature of 20C. The final situation is observed to be all water at 17C. What was the mass of the ice cube? C (al)= 900, C (water)= 4186, C (ice)= 2100 m(al)=...
  34. 4

    What is the Magnetic Flux Exiting a Cube?

    Homework Statement Here is the prompt: http://imgur.com/FTFz0fZ Homework Equations Magnetic flux = ∫B dot dA Net Flux for closed surface = 0 The Attempt at a Solution For part a: magnetic flux = (7.74 ^i + 4 ^j + 3 ^k)T * (0.254 m)^2 ^i = 7.74 T *...
  35. H

    Buoyant force on a submerged cube

    So a cube submerged in water will experience pressure on all six sides, and the pressure on the bottom will be greater than the pressure at the top (assuming there's gravity) and the cube will float to the top given that it has a low enough density. Something I'm curious about is what would...
  36. bsmithysmith

    MHB Using continuity to determine if there is a number one more than it's cube

    First off, it's: x = 1+x^3 Turned into function as: f(x) = x^3 - x + 1 From my understanding, we need to find an interval in which x will be one more than it's cube. Giving some points, I started off with (0,1), (1,1), (-1,1), and (-2, -5). Where I'm confused is how and where do I find the...
  37. Albert1

    MHB Divide a big cube into 49 small cubes

    Please divide a big cube into 49 small cubes
  38. N

    How do you calculate all the possible combinations on a Rubik's cube?

    I thought it would just be the number of faces multiplied by the nine cubes on each face? What am i doing wrong?
  39. R

    Cube tipping on horizontal surface

    Homework Statement A cube of mass m and side 2a is held on one of its edges on a horizontal surface. It is released from this position and allowed to tip. Find an expression for the angular velocity of the cube as its face strikes the surface of the table in the following cases: a) the...
  40. Saitama

    MHB Cube root of unity with a huge exponent

    Problem: Let $y=x/(1+x)$, where $$\Large x=\omega^{2009^{2009^{\cdots \text{upto 2009 times}}}}$$ and $\omega$ is a complex root of 1. Then $y$ is A)$\omega$ B)$-\omega$ C)$\omega^2$ D)$-\omega^2$ Attempt: I somehow need to show that the huge exponent is of the form $3k$, $3k+1$ or $3k-1$...
  41. W

    Finding the angular velocity of a cube about different rotation points

    Homework Statement A homogeneous cube of sides l is initially at rest in unstable equilibrium with one edge in contact with a horizontal plane (θ = 45 degrees initially). The cube is given a small angular displacement and allowed to fall. What is the angular velocity of the cube when one face...
  42. ShayanJ

    Metallic cube with circular hole

    There is a cube with its sides equal to d and its thikness equal to t. It also has a circular hole at its center with radius a (a<<d). Two sides of the cube are maintained at potentials V_0 and -V_0 . I want to find the potential inside the cube but I see no way for obtaining the boundary...
  43. P

    Tensor of inertia - hollow cube.

    Hi, Homework Statement I have found the tensor of inertia of a rectangle of sides a and b and mass m, around its center, to be I11=ma2/12, I22=mb2/12, I33=(ma2 + mb2)/12. All other elements of that tensor are equal to zero. I would now like to use this result to determine the tensor of inertia...
  44. NATURE.M

    Solving SHM of Cube Connected By Rubber Bands

    Homework Statement A cube of mass m is connected to two rubber bands of length L, each under tension T. The cube is displaced by a small distance y perpendicular to the length of the rubber bands. Assume the tension doesn't change. Show that the system exhibits SHM, and find its angular...
  45. M

    MHB Estimate the integral of g over the cube

    Hey! :o I have the following exercise: Integrate the $g=xyz$ over the cube that is on the first half-quadrant and it is bounded from the levels $x=1, y=1, z=1$. Having the following formula: $ \int \int_A{g(x,y,z)dS}= \int \int_D {g(x,y,z(x,y)) \sqrt{1+z_x^2+z_y^2}dxdy}$ do I have to take...
  46. N

    Equivalent Resistance of Cube of Resistors: A to B

    Homework Statement Here is a cube of resistors with each resistance of value "R".Find the equivalent resistance between A and B. Homework Equations The Attempt at a Solution My book says the equivalent circuit of the cube is : But i don't think it is correct.They have made parallel...
  47. L

    MHB Optimization of the sum of the surfaces of a sphere and cube

    If the sum of the surfaces of a cube and a sphere as is constant, deierminar the minion of the diameter of the sphere to the edge of the cube in cases in which: 272) The sum of the volumes is minimal 273) The sum of the volumes is maximum And the answer are 272 = 1 and 273 = infinit Ok Vs =...
  48. carllacan

    Moment of inertia of a cube along the diagonal.

    Homework Statement Calculate the moment of inertia of a cube which rotates along an axis along its diagonal. Homework Equations Moment of inertia definition: I = \int \rho (\vec{r}) \vec{r} ^2 dV Angular velocity vector; \vec{\omega}=\omega (\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}...
  49. J

    MHB Cube Roots: Solve A+B=C Problem Easily

    This is a simple question. The problem I'm facing is A cube plus B cube = 22 C cube A cube plus B cube over 22 = C cube At this junction I like to ask if I want to cuberoots both sides, will the 22 be cube root as well? I'm...
  50. C

    Is There More Than One Solution for Cube Root Equations?

    Lets say I was trying to figure out the restrictions of a radical equation and the function inside the radical was a cubic function. I know you have to make the equation inside greater than or equal to 0. In the case of a quadratic equation, you have to square root it once you bring everything...
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