Cube Definition and 610 Threads

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. T

    Dielectric Cube in a uniform electric field

    Hi. Those of you familiar with the classic problem in Jackson, where a dielectric sphere (diel const = k) is placed in a uniform electric field E_0, may recall the simple expressions for the field inside of the sphere: E_in = 3/(2+k) E_out. The solution tells us that the field...
  2. A

    Equilibrium and c is because ice cube is water so it will melt

    Hello there, I am unsure about the following question and would like some help to understand please! :smile: Consider the following systems: a) a container that is half filled with alcohol, stoppered and allowed to stand for several days b) crystals of KMnO4 that are dissolved in water...
  3. H

    Computing Modular Cube Roots Modulo a Prime

    Is there a good algorithm for computing such things modulo a prime? (I'll confess to not yet having tried to see if Shanks' algorithm can be easily adapted; I'll probably fiddle with that tomorrow)
  4. E

    Surface area of a cube with the length of each edge equal to x+1

    I am having trouble finding the surface area of a cube with the length of each edge equal to x+1. can some one help?
  5. D

    Mathematics behind Rubik's Cube?

    I've been trying to find this but I have no luck!
  6. H

    Suppose there is a cube and we can colour the cube's faces

    suppose there is a cube and we can colour the cube's faces with only two colours ..i.e. black and white ,,how many different patterns are possible...
  7. N

    Which cube members are not in the sequence and prove it?

    Which cube members are not in the sequence and prove it? 2, 5, 8, 11, 14, ... How can this be proved :cry: My answer: an = 3n + 2 Any natural number may be written as N= 3k+p for some natural number K and p=0,1 or 2. So N^3=(3k+p)3 N^3=3(9k+k^2p+kp^2)+p^3 N^3=3k+p^3...
  8. L

    Expressing Cube Roots Using Exponential Form e^{i\theta}

    I am asked to use the exponential form e^{i \theta} to express the three cube roots of: (a) 1 (b) i (c) -i what exactly does this question mean? I am really lost as to what they are asking for. here is a stab at it: (a) cube root of 1 is 1... so... would that mean... 1=e^{- \infty...
  9. J

    Express the edge length of a cube as a function of the cubes diagonal

    Hello, Here is my what am trying to solve. Express the edge length of a cube as a function of the cubes diagonal. Then express the area as a function of diagonal length if the side is x. This is what i know. The area of a cube is 6x^2 where x is the length. But in the problem i have...
  10. Y

    Ice Cube Melting & Anchor Thrown: Water Level Changes Explained

    1. When the ice cube melts, will the water level rise, stay the same or fall? and why? 2. What happens to the height of pond when ancor thrown overboard rise, stay same or fall? Why? I know that for the first question it's stay the same and for the 2nd question, it's fall; but i don't know...
  11. N

    If power were applied to a one meter cube of quartz crystal

    Is it true that, if power were applied to a one meter cube of quartz crystal and the crystal were driven to the breaking point, the gravity waves produced would definetly, 100%, be orders of magnitude too weak to be detected? Apparently Albert Einstein calculated that
  12. B

    Understanding Stoke's Theorem on a Cube: Exploring Surfaces and Normal Vectors

    Hi, can someone help me through the following question. Q. Use Stoke's Theorem to evaluate \int\limits_{}^{} {\int\limits_S^{} {curl\mathop F\limits^ \to } } \bullet d\mathop S\limits^ \to Here \mathop F\limits^ \to \left( {x,y,z} \right) = xyz\mathop i\limits^ \to + xy\mathop...
  13. B

    Friction problem on cube of mass

    a very small cube of mass m is placed on the inside wall of a funnel. The wall of the funnel makes an angle theta with the vertical axis of rotation (dotted line). The center of the cube is a distance r from the axis of rotation. the cube is held by static friciton. The funnel is then rotated...
  14. T

    How Does an Inverse Cube Law Affect the 2-Body Problem?

    Hello, everyone. Here is my question and my thoughts on it: Suppose we lived in a bizarre world in which gravitation, instead of being an inverse square law, were an inverse cube law. (a) In this world, show that the 2-body problem can be brought to a central force problem in a plane P by...
  15. Cincinnatus

    Exploring the Hilbert Cube: Understanding its "Cubelike" Nature

    So, what exactly is "cubelike" about the hilbert cube? I think I am having trouble "visualizing" it. Is it just called that because it it homeomorphic to I^inf. ?
  16. P

    In a race down inclined plane why does a cube reach bottom first?

    In a race down inclined plane why does a cube reach bottom first? The other object is a solid cylinder. The cylinder rolls without slipping, and the cube slides. The cylinder has radius R, and a cube has radius R. Does this depend on the mass of the objects? Is it because since the cube...
  17. M

    Solving a Cube Problem with Constant Coefficients

    hi all i have a bit of a problem here, it has to do with completing the cube. here is the problem y''' +y' + 2y = 0 i am trying to sove by the methoed of constant coefficients
  18. I

    How Does a Cube Exhibit Rotational Motion?

    rotational motion I have a problem with describe rotational motion for the cube, i met the rotational motion for the circle shapes but cube is somthing new, so if u know any sources, exampels or solution and book where i can find descirbe of rotational motion for cube pliss give me a sign or...
  19. S

    Find Electric Flux and Charge in Cube with Edge at (0,0,0)

    I know I'm reposting this... but no one seems interested in my thread.. maybe becuase it already has replies (which doesn't mean its been solved!) but whatever cube is placed with its edge at (0,0,0) as in the diagram. The sides of the cube are1 .4m. Find the electric flux and the charge...
  20. S

    Rotational Inertia of Rectangular Cube in a Hoop

    i know that the equation for rotational inertia of a hoop is different than the equation for a solid cylinder, but what is the equation for a rectangular cube in a hoop? _ \ -> \ (|) <--is what I mean if the diagram helps at all <-
  21. U

    Does Melting Ice Change the Water Level in a Glass?

    Some help with this question please? a) An ice cube floats in a glass of water. When the ice melts, will the water level in the glass rise, fall, or remain unchanged? Justify your answer. b) If the ice had been made from pure water, and the water in the glass was salt water (denser than...
  22. A

    How can group theory be applied to improve Rubik's cube solutions?

    I've always been fascinated by Rubik's cube. I have developed solutions for it and all the related cubes 2x2, 3x3, 4x4, 5x5. For me the cube it is to group theory (of a partcular type of group) what a slide rule is to real arithmetic. Even "laboratory" might not be too stong a label for...
  23. M

    Find the net amount of charged contained in a cube

    Hello everyone I'm confused on where I should go next with this problem. It is found experimentally that the electric field in a ceritan region of Earth's atmosphere is directed vertically down. At an altitude of 300m the field has a magnitude 60.0 N/c; at an altitude of 200m, the magnitude is...
  24. A

    Particle Mass m in Cube Box: Density of Eigenstates

    Consider particle of mass m in a cubic box of length L which has energy spectrum given by E=(k sqr)/2m =2 (pi sqr) (nx sqr+ ny sqr +nz sqr)/m (L sqr).what will be the density of states (eigen states per unit energy interval) k is boltzman const..nx,ny,nz are unit vectors in resp. directions...
  25. A

    Balancing a Cube on its Corner

    Say that you have a box with mass "M." The base is given by vector "v" and height by "w." If you want to balance it on the corner, what should the angle between "v" and the surface be (image attached)? I tried to write this out, but not sure if I did it correctly. I figured the torque...
  26. M

    Is There a Cube Inscribed in a Sphere with All Black Vertices?

    Can anyone help me with this problem? Suppose a sphere is colored in two colors: 10% of the surface is white, and the remaining part is black. Prove that there is a cube inscribed in the sphere such that all vertices are black thanks ~matt
  27. D

    What Is the Resistance of Each Resistor in a Modified Cube Circuit?

    Imagine a cube where all sides have a resistor, now remove one resistor from it and replace it with an ohmmeter, the ohmmeter reads 100ohms, calculate the resistance of each resistor. By the way each resistor is the same value. How do you go about doign this question?
  28. C

    Comparing dQ/dt & dT/dt of a Cube & a Globe

    If there is a globular object and cube which have the same volume and you heat both of these objects in same amounts of heat and leave these to cool down 1)dQ/dt of which one is higher? If so why? 2)dT/dt of which one is higher? if so why? t-time Q-energy T-temperature
  29. A

    What is the General Method for Deriving Cubic Roots?

    I've been trying to derive general solutions for cubic roots, i.e. the general solutions of (will Latex just work?) $ax^3+bx^2+cx+d=0$ I do not want to be shown the solutions - but does anyone know what direction to go into achieve this? I thought I'd found solutions at one point but...
  30. T

    Georgia Tech Lecture: Time Cube with Gene Ray

    Well, this Thursday, on my birthday, "Dr. Gene Ray, Wisest Human" will give a lecture on his Time Cube theory. If you have not heard of it, look here: http://www.timecube.com/ . If anyone can decipher what he is talking about, please share your thoughts with the rest of us and explain it...
  31. G

    How Is the Net Charge Calculated in a Cube Within a Vertical Electric Field?

    In a region of fair weather, the electric field is found to be vertically down. At an altitude of 400m E=20 N/C at 200m E=90 N/C. Find the net charge contained in a cube 200m on and edge, with horizontal faces at altititudes of 200m and 400m. I wasn't sure where to start so i used coulumbs...
  32. F

    Finding Probability of Solving a Rubik Cube with 3 Pieces

    Dear friends, I need some help with this problem. "What is the probability of building a solvable rubik cube only by ordering randomly all pieces but three"(let us suposse that these 3 pieces are vertices) That is you first get a random cube without three vertices and then you try to build...
  33. T

    What is the mass of the ice cube?

    take an ice cube at 0 degrees C and place it in 500 grams of water at 60 degrees C . The final temperature is 18 degrees C . What is the mass of the ice cube? heat of fusion for water is 80 cal per g. Anyone?
  34. C

    Is Rubik's Cube Worth Our Time?

    Hi everybody, I am sure this has been talked about before but I still want to ask: is Rubik's cube worth our time? I mean is it really worth spending hours/days/... trying to solve it?I have been trying for some time but i haven't found the solution yet. It's really challenging in my opinion...
  35. J

    How Do You Solve a Leslie Cube Assignment?

    sorry, this was my question from yesturday, and now my assignment is due tomorrow. anyone have any help for me? A Leslie cube has a surface temp of 97C. One of its four side faces has an area of 100 cm^2 and is painted black. Calculate: a) the wavelength at which the spectral intensity...
  36. J

    Calculating Radiation from a Leslie Cube

    A Leslie cube has a surface temp of 97C. One of its four side faces has an area of 100 cm^2 and is painted black. Calculate: a) the wavelength at which the spectral intensity (per unit wavelength) is a maximum b)the total intensity (all wavelengths) of the emitted radiation just outside...
  37. V

    How do I determine the work done by an ice cube?

    Hi, I need some help with my thermal physics. I posted these questions on the high school forum (I'm just a junior in high school), but my physics teacher takes questions out of college-level books, so I thought it would be more appropriate if I posted here. The two questions are: 1. An...
  38. recon

    Find the Largest Cube Volume on n x n Paper

    If I were to draw a complete, continuous net of a cube on a piece of paper measuring n by n, how can I proceed so that the resulting cube has the largest possible volume achievable from that paper size? I know that the most obvious solution (at least to me) is to draw the net along a...
  39. F

    How Many Configurations Does a 2x2 Rubik's Cube Have?

    Hello everybody! What's the number of possible configuration of a Rubik cube 2x2 (allowed movements are like in a 3x3 cube but here there are not central pieces that don't move). THanks for your help
  40. A

    A little inverse help cube root

    find the inverse of f(x)=3sqrt(x+2) -7 x>=-2 I got this far (x+7)=3sqrt(y+2) I don't know how to get rid of the cube root someone help please :cry:
  41. A

    Elastic Collision of Rod and Cube: Dynamics Unveiled

    Consider a cube of uniform density, mass M, sidelengths 2a resting on a frictionless plane. Origin is placed in the cube's center. A rod of length L, attached to the ceiling z=a+L, mass m, hits with its tip the corner (-a,a,a) on the side x=-a with velocity V_{0}\vec{i}. Determine the...
  42. T

    How to Prove This Limit with Cube and Fourth Roots?

    Hi guys, I have another limit I can't move with. Well, I guess it goes to zero, but can't show a bulletproof evidence: \lim_{n \rightarrow \infty} \frac{ \sqrt[4]{n + 2} - \sqrt[4]{n + 1}}{ \sqrt[3]{n + 3} - \sqrt[3]{n}} Even after I got rid of denominator, I can't find some known...
  43. J

    Find Equation for Ideal Gas in Cube Container

    Hello, I am having some difficulty following the method for finding an equation for an ideal gas. There are a few different forms, but I'm proving 1. For an indiviual particle of a gas in a cube container side length L, it is traveling with a velocity of u1 on the x-axis (its x component of...
  44. M

    Calculating the Landing Positions of Two Cubes on a Frictionless Incline

    Say I was wondering if I could maybe get some help with this problem. In a physics lab, a small cude slides down a frictionless incline as shown in the figure below, and elastically strikes a cude at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is...
  45. C

    Calculating Cube Deceleration on a Moving Board

    A 0.5m cube is sitting on top, and at the end, of a 1m wide by 3m long board. Both the cube and board are traveling at a constant velocity of 10 m/s. The board begins to decelerate at -8.5 m/s squared. The cube decelerates across the top of the board at -3 m/s squared. How much time will it take...
  46. J

    What Changes if the Earth was a Cube

    How would life on Earth charge if the Earth was a cube instead of a sphere? ...We're suppose make points on how things would change according to Newton's laws and stuff... Well first thing I noticed is that gravity at the Earth's surface wouldn't be constant anymore would it? Because...
  47. P

    Flux through a cube with non uniform electric field

    This is really frusterating me, my book provides horrible examples and i have no idea how to go about this problem. There is a cube with sides L= .3m and an electric field = (-5 N/C X m) x i +(3 N/C x m) z k i= i hat k= k hat I know that the flux = the integral of the E ...
  48. C

    Find the length of the side of a cube of iron

    Iron has a property such that a 1.00m^3 volume has a mass of 7.86 X 10^3kg(density equals 7.86 X 10^3kg/m^3). You want to manufacture iron into cubes and spheres. 1.) Find the length of the side of a cube of iron that has a mass of 480 g. 2.) Find the radius of a solid sphere of iron...
  49. E

    Find Friction for Cube on Rough Floor

    Need some feedback on my attack strategy to the following: A cube of side L rests on a rough floor. It is subject to a steady horizontal pull, F, exerted a distance h above the floor. As F is increased, the block will either begin to slide, or begin to tip over. (a) What must be the...
  50. X

    Cube Question In Space Geometry

    Hey everyone, I came across this rather "uncoventional" space geometry question, from a dutch book. I have answers in mind but I want to check with you guys.. Check the attached picture for the cube.. The question goes like this: This photograph of a cube was taken on a tropical island...
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