zoharjackson.com -Hyoer cube

Hyper Cube: - Ben Tupper        A teseract is a 4d cube. I'm not exactly sure the distinction between a hypercube and a teseract, but as far as I understand, a testeract is the actual 4d cube (in 4-space that is) while a hypercube is the 3-space portrayal of that teseract. it as a "cube" in three space is to a picture of a cube in 2-space: a hypercube is a picture of a teseract in 3-space. The theory behind going up spatial di'mensions is creating right angles (or normals) to all previous points. One starts in 0-di'mensions with si'mply a point that takes up no area. Because all there is, is one point, any line segment drawn from it is necessarily its normal. That is then one di'mension. After drawing a second right angle at each end of that line and connecting the ends of the line segments, one gets a square: 2d.        Drawing a third right angle from each of the corners of that square will create a cube: note that the right angle is the normal to both the up and over lines in the original square. From there, in 3-space at least, we get stuck: how can we draw another right angle to all three of our previous right angles?? It’s i'mpossible! Any line coming out from the corner of the cube cannot possible be 90 degrees from all of the three lines coming out of that point! therefore, in making a hypercube, we do what we would when we try to draw a picture of a cube: when proceeding in the latter activity, because we cannot draw the "out" line on paper, we symbolically draw a line on an angle and your brain sees this extra line as an "out" line even though it is technically not 90 degrees from the other two lines coming out of that corner of a square. So in 3-space, when we try to draw another right angle, since we cannot, we put it at a different angle that is not right, rather diagonal, to symbolize a fourth right angle. In doing this, we extend line segments from each of the corners to create another cube when we connect them all (analogy: when we extend another line off of each corner of a square and connect them, we form another square; i.e. the other side of the cube).        Actually, the final creation of a hypercube creates eight cubes, just as creating a cube makes six squares and creating a square forms four lines. a line, too, has two points at each end. If you look carefully, you can see all the cubes inside the hypercube, albeit, some slanted and obscured, but they are all there. --Written by: Ben Tupper