In that blessed region of Four Dimensions, shall we linger at the threshold of the Fifth, and not enter therein?
Now in order to establish a position in a space of four dimensions it would be necessary to measure in four mutually perpendicular directions.
For the sake of convenience, let us call the figure we are investigating—the simplest figure in four dimensions—a four-square.
Having thus seen how it is possible to describe the properties of the simplest shape in four dimensions, it is evident that the mental construction of more elaborate figures is simply a matter of time and patience.
Thus, just as by handling or looking at it, it is possible to describe a figure in space, so by going through a process of calculation it is within our power to describe all the properties of a figure in four dimensions.
Extending this to four dimensions of space, we obtain an exact analogue of line geometry, in which (i.
By projecting this quadric stereographically into space of four dimensions we obtain Klein's analogy.
The space of points and planes is of three dimensions, but the space of lines is of four dimensions.
Let us pursue the analogy by showing what dwellers in four dimensions might do.
Another possibility in space of four dimensions would be that of turning a hollow sphere, an india-rubber ball, for example, inside out by simple bending without tearing it.
But the dweller in four dimensionsof space will fit them together without any trouble.
Webber that he had found people alive in the world who could actually see in four dimensions, live in four dimensions, think in four dimensions?
The conclusion, with respect to the quantity A^4, has been that it should represent a space of four dimensions.
It may be even possible for the mind to function normally in a space of four dimensions.
Nothing then prevents us from imagining that these operations combine according to any law we choose, for example, so as to form a group with the same structure as that of the movements of a rigid solid of four dimensions.
The above list will hopefully provide you with a few useful examples demonstrating the appropriate usage of "four dimensions" in a variety of sentences. We hope that you will now be able to make sentences using this group of words.
