Such as two point straight line length, the area size of three points, four points size, are good, then the higher the "volume"?
CodePudding user response:
Several inferences [not prove (I'm not only prove and validation)]By: 1. The bottom contour rectangle area such as triangle area=1/2 and pyramid bottom area such as area, such as volume size=1/3 of the bold guess "4 d pyramid"=volume equal to 5 points to where the other four points space distance * 4 points in the space volume/4
Five points "6 d pyramid"=sixth volume of the distance to the other five dimension * five points in the dimension size (i.e., the volume of the ball above)/5...
Now is another question, what's the distance is the distance from a dimension?
Again observe equation of low dimensional space for any more artful [points to the straight line distance formula, and point to the distance formula] (this I am quite sure there must be very beautiful and can derive the representation method of extension, but also don't know)
Then you can calculate,
, of course, the above said there are two premises, 1: only use n point says the "volume" n + 1 d, 2: the n point really can show a dimension of n - 1 "volume" [as three points are not bound to siege as a 2 d triangle]
CodePudding user response:
Multidimensional and a basic knowledge: n can find vector set has n elements {a, b, c... }, and any element of n - 1 other elements is not adjustable, together to get [b, c is not a vector... addition, subtraction, multiplication, and division]Can be used in the coordinates, said
{a, 0, 0... }
{0, b. Zero... }
{0, 0, c... }
Spirit likeness matrix, so the computing tools to participate in some inferences may be able to use matrix, computing