# cube

1. ### Calculation of electric flux through a face of a cube.

A charge q sits at the back corner of a cube, as shown in the attachment. What is the flux of \mathbf{E} through the yellow shaded side? The way I thought fro proceeding was that should take differential area element d\mathbf{A} in the yellow face, now the direction of this element will...
2. ### The length of an edge of a cube

Dear Forum Members: Can anyone give me an algorithm for finding the length of an edge of a cube, given the volume of that cube? Thank you.:) Best regards, Carl James Mesaros
3. ### Cube inside sphere

The largest cube that can fit into a sphere must have eight vertices touching the surface of the sphere. Express the side length, s, of the cube in terms of the diameter, D, of the sphere. Posted this in the elementary forum, but realised there was an algebra forum, anyway quick responses...
4. ### Cube, induction, block

The cube S with side 2 consists of 8 unit cubes. Define block a figure that is formed from a cube S as a result of the removal of one unit cube. Decide if the cube with dimensions 2^nâ‹…2^nâ‹…2^n from which one cube has been removed can be built by blocks. Since a block is formed by 7 unit...
5. ### Irrational equations with cube roots

\begin{aligned}&\sqrt[3]{x+1}+\sqrt[3]{3x+1}=\sqrt[3]{x-1}\\ &\Leftrightarrow(x+1)+(3x+1)+3\sqrt[3]{(x+1)(3x+1)}(\sqrt[3]{x+1}+\sqrt[3]{3x+1})=x-1\\ &\Rightarrow 3(x+1)+3\sqrt[3]{(x+1)(3x+1)}\cdot\sqrt[3]{x-1}=0\ \ldots\ x=-1\end{aligned} The part that confuses me is the implication. How...
6. ### Edgy cube's faces paths

How many unique paths can one start at each face of a cube and move square by square (only to unused squares of shared edges) until all six faces are included?
7. ### Cube with spheres bumping within

Take a cubic box of edge E, wherein two spheres of like diameter and mass bounce elastically. Will the box move randomly or not?
8. ### Polygons in a cube

Hello, the situation is the following: A cube is intersected by a plane. Depending on the coordinates of the plane, different polygons can be created by the intersection. How can I prove (with analytic geometry) that these polygons can be triangles, rectangles, pentagons or hexagons...
9. ### Latin Cube

Hi, I made a puzzle game called Cubicks. When you finish the puzzle you get a result like this: Making the puzzle game cost me 9 months of free time, but I found it easier than solving the problem how many Latin cubes there exist. A Latin square is a square like a Sudoku where in...
10. ### Cube center inverted through sides

A cube can be divided into six equal, regular right pyramids. What outward shape results when their bases form an empty cube, that is, when their apexes are inverted through their bases?
11. ### finding the cube of large numbers?

Is there a way to figure out these larger numbers I get how to do the variables though so far. Thanks.
12. ### Cube outline -- all edges visible?

What is the proper term for a (non-solid) cube outline with all its edges delineated (and sometimes representing an optical illusion)?
13. ### How many sides does a tesseract (4D Cube) have?

I could guess but I can't seem to find the answer any where. Interestingly enough I think one of the standard IQ questions is to count how many sides a shape has, so I definitely don't want to guess ;)
14. ### Cube vs. square

Is there a cube number and a square number whose difference is 5?
15. ### Distances between matrix-slices in a cube

I'm trying to find a good way to represent a distance matrix D where each i-th, j-th value of this matrix is the distance between matrix-slice i and matrix slice j. I asked on MSE (with better detail) but haven't heard a response yet: linear algebra - Optimized Distance Calculation for Data...
16. ### How many red cube can surround a blue cube?(all equal size)

Question taken from--> https://brilliant.org/profile/calvin-8u8hog/sets/calvins-picks-level-5-challenges-2015-xxiii/299119/problem/he-was-wrong-too/?group=3BX9rjPrQ3CM You have a (solid) blue cube and an unlimited amount of (solid) red cubes, all of which are of the same size. What is the...
17. ### cube flux

calculating the flux of cube length's S, centered at the origin, with the field being: F=x^2(i)+y^2(j)+z^2(k) So the flux of the face of the cube in the (i) direction : F dot dA(i)= x^2*dA...but x at this surface is just S/2( cube's center is at origin) , so it (S^2)/4*dA, and dA is...
18. ### cube roots of unity

hi what am i missing here........ one of the cube roots of 1 is cos 120 + i sin120. check: (cos 120 + i sin120)^3 = cos 3600 + i sin360 = 1. however when i do this in cartesian form: cos 120 + i sin120 = -1/2 + i(sqrt 3)/2 check: [-1/2 + i(sqrt 3)/2 ] = -1/2 - i(sqrt 3)/2 as opposed...
19. ### Spacediagonal 30 cm in a cube? Calculate the cubes side lengths?

Hi! I have this question about an exercise in my Swedish math book. It told me to calculate the cube's side lengths. But the only thing I know is the spacediagonal. Or whatever it's called in English. I think that it has something to do with Pythagoras theorem. First I thought that it was that...
20. ### cube

You know the integer triangles? I used those to form a cube. (2mn)^2+(m^2-n^2)^2+(((m^2+n^2)^2-1)/2)^2=(((m^2+n^2)^2+1)/2)^2 Think of a 3 4 5 triangle combined with a 5 12 13 triangle, using the hypotenuse of the first triangle to generate the second triangle. Remove the 5 and the 13. So a...