Question

vectors in a cube
http://prntscr.com/4qavd0

Answer 1

#11 and #12

Answer 2

@xapproachesinfinity @tinybookworm

Answer 3

for #10 :
i+j gives diagonal for the face in xy plane

Answer 4

#11 The four others are (1,1,0), (1,0,1), (0,1,1), and (1,1,1)

Answer 5

Oh I see, so its basically taking all combinations of 0,1 for each axis is it

Answer 6

Correct!! :)

Answer 7

2x2x2 = 8 corners

Answer 8

was just trying to see if this helps in answering next question on cube in 4 dimensions which looks totally mysterious

Answer 9

i think i can work rest of the #11 question
any ideas on #12 ?

Answer 10

Yes, actually, I have never learned about 4D.

Answer 11

oops ran out of time!

Answer 12

@xapproachesinfinity #12 please

Answer 13

a cube is a cube in any dimension well except you can't draw a cube in 2 dimensions or lower.
so if a cube is a cube in any n-demension (where n>=3) wouldn't it always have the same amount of corners, edges, and so on...
I can't image a cube any other way.
I could be wrong.

Answer 14

i can't imagine it in other dimensions either, but this problem set is from gilbert strang.. so im thinking he might be having something in his mind when creating this problem

Answer 15

@rational @xapproachesinfinity @myininaya This is what I found out.
http://math.stackexchange.com/questions/16366/linear-algebra-cube-dimensions-3
I find it hard to understand. How about you?

Answer 16

going thru..

Answer 17

Wow! they are working corners in the same way we have worked earlier :
2x2x2x2 = 2^4 = 16

16 corners

Answer 18

The four dimensional cube is apparently called the tesseract .
http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/four_dimensions/
So I guess they are still calling it a cube.

Answer 19

Yes. I find it hard to imagine "8 3-dimensional sides"

Answer 20

By the way @rational I think you should read that link.
I think you will find what you are looking for.

Answer 21

thanks @myininaya and yeah this problem is picked from a very old edition so there might be some new terminilogy now

Answer 22

it seems they're just stretching a cube out of 3D space(not possible imagine) and joining the 8 corners of one cube with the other cube

Answer 23

like we stretch a square perpendicular to the plane to create a cube

Answer 24

do you think this is not the cube we should be imagining?

Answer 25

@myininaya Haha, agree

Answer 26

"cube"*

Answer 27

in that link, they are creatign tesseract by stretching a cube out of 3d space

Answer 28

stretch a line out of 1D ---> you get a square

stretch a square out of 2D ---> you get a cube

stretch a cube out of 3D ---> you get a tesseract

Answer 29

thats how i am interpreting the earlier link... it doesn't fully makes sense, but i am getting correct numbers for corners/faces/edges using that model xD

Answer 30

Yes, and in 4D we strech the cube not to one direction but six.

Answer 31

http://en.wikipedia.org/wiki/Hypercube
here some pictures where we have more n-cubes

Answer 32

these cubes look crazy

Answer 33

@myininaya Yes they are. I think I will try something different, not professional math.

Answer 34

http://upload.wikimedia.org/wikipedia/commons/d/d7/8-cell.gif

indeed it looks crazy, wish god gave us hardware in our heads to imagine this xD

Answer 35

Haha. My head is spinning like those cubes.

Answer 36

even after a rotating figure is giving i can't seem to process what kinda n-cube that is
i think it might be the 4-cube one

Answer 37

yes it is a 4-cube projection into 3-space, looks like a very interesting subject to spend time in xD