So you are saying if you start out with a point , and project or move the point in a perpendicular direction , you get a line . Then you project that line in a perpendicular direction and you get a square , then if you project that square in a perpendicular direction you get a cube , then if you project the cube in a perpendicular direction you get a hypercube , a 3D representation of a 4D object , is this correct ? So that you have a Larger cube (the new dimension?) surrounding a smaller cube , and all points projected are connected . So the surrounding objects of this cube are like pyramids with the top chopped off .
My question is , in what direction is the cube projected ? Are all 8 points projected outwards ? I can visualise that quite easily in a 3D sense , but it still is hard to percieve this new cube as a new dimension .
Okay , thats what i first thought about hypercubes , but then i saw this link
http://www.well.com/~abs/SIGGRAPH96/4Dtess.html which tries to explain the formain of a hypercube from a 4D beings perspective . The hypercube is made of 8 cubes supposedly , but when looking at this picture i see only 7 hexahedrons .http://www.well.com/~abs/SIGGRAPH96/Fig6a.gifI think maybe the last one is the entire cube correct ? But then , the surrounding cubes arent actualluy cubes to us . But to a 4d being they are , so to us 3d beings , our inability to visualise the 4th dimension forces us to almost fold it in with the other 3 dimensions . Or atleast thats how i try to think of it . The 4D is the joining of the cubes to look like hexahedrons .
Atleast thats the conclusion i have drawn from that links explaination .
EDIT : I did a bit more searching and found this :
http://members.aol.com/jmtsgibbs/draw4d.htmIts a 3d java visualisation of a hypercube . But you can rotate the hypercube , firstly around the 3 normal dimensions , but also along the 4th dimensions . The scrollbars on the far left , near left and top control this . Now when i manipulated them along the 4th axis , i was completely stumped . And im guessing everyone else is , because i cant visualise this object rotating , atleast not yet . Maybe if i play with that thing long enough it will hit me .
It also lets you do other polytopes , though i havent been game to try the others yet .
This message has been edited by Darkmatic, 11-26-2005 10:53 AM