why is it not possible to draw a four dimensional figure?
469981
You can draw any n-dimensional object via Parallel Coordinates.   \nThis version of drawing starts with equidistant parallel lines as each axis (i.e. x-axis, y-axis, etc.)  and you graph the points on that axis.\nHere is a great site on it: http://catt.bus.okstate.edu/jones98/parallel.html\n\nSome people I know claim to be able to draw four-dimensional objects that kind of rely on parallel coordinates.  They draw the standard three-dimensional grid (each axis is perpendicular to each other) and they put that WHOLE grid on top a number line to represent the fourth dimension and slide it to the fourth dimensional coordinate (like time factor).  Kind of like parallel coordinates (which starts with 1-dimension and onward)  except you start into 3-dimensions and then add a fourth.
160693
You must think about the 3d visualization of 4d objects as partials projections or perspectives (as well as when you represent a cube drawing it on a paper sheet, you only describe some of its properties by analogy): so you cannot "see" 4d objects: you can only describe them.\n \n\nSee this link for a rough idea of an hypercube (there would be much more to say about it ...)\nhttp://answers.yahoo.com/question/index;_ylt=Apvwu5u3VyjMZfW_mDnnJUnsy6IX?qid=1006012001214\n\nSee this other one (expecially the links in all answers) for the so-called "Klein bottle"\n\nhttp://answers.yahoo.com/question/index;_ylt=As6vB06qMWLWdUaS3dhCfW_sy6IX?qid=1006013107146\n\n\nfour dimensions is interesting in maths because (they say: I'm starting now to study it) that there are many different "regular solids" which you can hypotize counting sides, vertexes and faces. From 5th dimension on, there is only one kind of regular solid, so it is not considered an interesting field of study.
30239
You can't just draw one? It's 10 boxes across the top and down the side, starting with 0 and going to 9 (and no, the corner doesn't share both sides). All you need are a pen and a ruler.
999626
there is no end 4 d world
486295
The four-character form IIII creates a visual symmetry with the VIII on the other side, which IV would not.\n\nEither IIII or IV is acceptable for 4, so I guess the "eyes" have it.
585241
the sensors we have in our body are only able to detect the 3 dimensions that we see. some physicists think that there are up to...11? dimensions existing, however we are unable to detect them and therefore...its not possible to "go" there. the same as we are not able to "go" into a 2D world...unless someone has figured out a way to become flat
89075
Our universe consists of four dimensions: three of space and one of time.  This leads many people to think that the "fourth dimension" refers to time, and higher dimensions must be associated with something else.  That isn't true.\n\nTheoretically, there is no limit to the number of possible dimensions, whether spatial or otherwise.  Another universe might have six dimensional space and two dimensional time, for instance.  We can't imagine such a place, but using math, it's pretty easy to describe its properties.
789597
Mathematically n dimensions can be described but our experience is only 3 dimensions So the properties of fourth dimensonal shapes can be mathematically described and a fourth dimensional quantity that is in units^4 can also be calculated\n\nThis is an argument that the 4th dimension is time. That cannot be the case when one considers the properties in 3d are L, L, and L One would immediately envisage that the 4th, 5th .... nth dimensions would also all be L\n\nA tesseract, the 4 dimensional equivalent to the 2 dimensional square and 3 dimensional cube, is not a time related object at all. Its 3D projection can be build and the objects equivalent of a 2D shadow seen easily. In 4-space it occupies L^4 units^4. Wikepedia has some interesting information and projections of a tesseract
792546
To my knowledge, those coordinates are given in pixels, and there is no way to draw something "between" the pixels. If you character seems like they are jumping around rather than walking smoothly, try only incrementing your X and Y coordinates by 1 or 2 pixels at a time\n\nYou may also need to make sure you increment them slower. If you are incrementing them by 1 but doing it every 50 milliseconds or so, it's going to look very jumpy\n\nHope that helps.
129006
I asked this a couple weeks ago:\nTo answer your question:\nVector graphics are composed of curves connected by points, mathematically defined. A circle is four curves connected by four points. A rectangle is four curves, connected by four points. (No, that wasn't a typo...they are considered curves even though they're straight lines. No, I don't know why...math and I never really got along all that well.) When you want to make the circle larger or smaller, the mathematical formula is redefined, and the circle keeps it's perfect crisp lines. Creature House Expression, Macromedia Freehand, and CorelDRAW are three examples of vector programs. These programs are considered object oriented because everything you make, even text, is an object that can be manipulated independent of other objects and the background (which can also be an object if you put something there, such as a rectangle covering the page.) You can arrange them so they are in front of each other, in back of each other, stack them, or group them. Vector programs are also sometimes called drawing programs, while programs like Adobe Photoshop and Procreate's Painter are paint, or raster programs.\n\nA raster program constructs what you see on screen by using pixels. When you enlarge the picture, the only way it gets bigger is for the pixels to get bigger too, and you lose the nice edges. So when you work in a raster program your best bet is to make your picture the size at which you'll ultimately be using it, because you will be limited in how much sizing you can actually do. And that is the beauty of working with vectors! You can work on a 4" object and enlarge it to 4' if you want. And it'll look just as good at 4' as it did at 4".\n\nSou
196942
wow, that's pretty amazing.  i was convinced that was wrong until i tried drawing the "counterexample" i had in my head.  other than reading through that proof (props to the guy who posted that link, btw) i guess the best way to realize this is true is to show that for any five closed shapes in two dimensions, there will always be at least two shapes that do not touch one another.  because of this, you can color those two shapes the same color, so you will have a maximum of four colors.\n\nthis problem is reducible to a graph with five nodes, where each node represents a shape and each edge represents a shared boundary.  (showing that this is reducible to this is probably the difficult part of the proof, which is why i'm glossing over it).  you cannot connect each node to every other node without there being at least one set of intersecting edges.  if edges intersect, it indicates that the shapes (or countries) represented by the two nodes connected by one of the intersecting edges do not share a border.\n\nhere's my suggested proof (assuming we accept the reduction to this graph problem):\nstart with a graph G with three nodes, {A, B, C}.  There are also edges {AB, BC, AC}.  So, G is a closed graph with three nodes and three edges where each node is connected to each other node in the graph (i.e. G is a triangle).  If our reduction of the coloring problem is correct, then there exists a map reducible to this graph that requires three colors to be colored in the described way.\n\nNext, construct a graph H by adding a node D to graph G.  There are two possible ways to add D: 1) D can be on the interior of closed graph G; or 2) D can be outside the interior of G.\n\nIn case 1, let the new graph with nodes A,B,C,D be called H.  We need to show that we can make H such that D is connected to A, B, and C without any intersecting edges.  This is simple enough; straight edges to A, B, and C from D do not intersect each other or the existing edges of the graph G.  So, H demonstrates that a map can require four colors.  H now has four separate enclosed interior regions: triangles ABD, ACD, BCD, and ABC.\n\nFrom H, construct a graph I by adding another node E.  Repeating the above procedure, E can be placed in four places: a) in the interior of ABD; b) in the interior of ACD; c) in the interior of BCD; or d) on the exterior of ABC.\n\nCASE a: As with constructing H, edges can be drawn from E to A, B, and D.  However, C is on the exterior of ABD, so any edge from E to C must cross either AB, BD, or AD.  So, in case a, there must be an intersection, so four colors is still an option.\nCASES b and c follow similarly.\nCASE d: E is on the exterior of ABC, but D is on the interior of ABC.  Any edge between E and D must intersect AB, BC, or AC.  So, coloring with four colors is possible in this case.  Since it is possible in all cases, it is possible for any map with five regions with a sub-map reducible to a graph like H.\n\nCase 2) Instead of placing D in the interior of G, make a graph H' by placing D on the exterior of triangle ABC.  Any quick drawing will show that D is easily connected to A, B, and C.  So there is a map with four regions that requires four colors.  To make the rest of this easy, note that H' also produces four enclosed regions: ABD, ABC, BCD, and ADC.  I won't go through the trouble to prove this, but clearly H' is isomorphic to H.  That being said, whatever is true of the general graph H is also true of the general graph H'.  Therefore, a graph I' made by adding a node to H' cannot be complete without there being at least one set of intersecting edges.\n\nSince this is true for all cases, any map reducible to a graph with five nodes is colorable with just four colors.  QED\n\nSorry this is so long.  I hope it's helpful.
1112728
to draw lines u hav to select 2 points at a time (as no 3 r collinear)\n\nthus no of selections of such points is nC2= n!/ [ 2! (n-2)!]
955988
Well, almost every engineered product such as cars and bridges and rockets and even iPods require drawings to show how they're going to be made.  Even for 3D objects, those drawings are still largely 2D, and 2D geometry is indispensible in the development of those 2D drawings.  This is true even for computer workstations that work with 3D representation of products, because all the cross sections are still 2D, and engineers need those cross sections to help with the analysis.
511866
can not draw in answers
672629
Make a 3d model and print it out using anim8or @ anim8or.com\n\nIf that is not in option, try using a styrafoam block and carve it.
1022630
None of those are "planes".\n\nA plane is drawn as a square simply because of the limitations of a sheet of paper.\n\nA plane is infinite in two directions.  It has no start or end point on the xy axis.  A sheet of paper of course does have start end end points.  Usually 8x11\n\nNone of rectangels, squares, or triangles are planes.  They are all subsets of them.  And darned small ones at that.\n\n-Dio
859983
um....no.  We can't readily draw on here.  Second, how can we summarize our drawings, if we can't draw on here.  There are a lot of websites that talk about the 4 main network topologies.  I suggest you search for star, bus, token ring, mesh.