Visualising the 5th dimension - Mathematics Stack Exchange
2017年5月19日 · 1. A point is zero dimensional. If you extend the point by smearing it through one dimension, you get a line segment. The line segment is the one-dimensional version of the zero-dimensional point. Now, take that line segment, and smear/spread it in a different dimension, orthogonal to (i.e. at a right angle to) the first dimension.
Rotating 5-Dimensional Cube : r/GeometryIsNeat - Reddit
2023年12月6日 · A 5-dimensional cube projected down to 2-dimensions. The cube is rotating in 5-dimensional space along ...
geometry - What is the volume of an n-dimension cube?
2021年4月1日 · In the first dimension, the volume would be just the side length or a= a1 a 1. For n=2: This would be the square whose side length is a and the area is a2 a 2. For n=3: This would be the cube with volume of a^3. For n>3: I could do an induction proof on the conclusion, however a more intuitive pattern starts to emerge: having the dimension be 0 ...
4d, 5d, 6d ... 11d equivalent of cube? - Mathematics Stack Exchange
2012年10月14日 · The prefix "hyper" is often used for higher dimensional versions of geometric objects. Look up hyperplanes, hyperspheres, and hypercubes. This does not give any clarity about what dimension is intended though; just that there is the potential for the dimension to be greater than 1, 2, or 3.
ELI5: What exactly is the 5th dimension? : r/explainlikeimfive - Reddit
It depends on how you define it. A dimension is simply an index on a vector. You could have 5 dimensions defined as torque_xy, velocity_z, time, displacement_yz, rotation_z. There is no the fifth dimension. If you're talking about what a 5th spatial …
geometry - How many verticies, edges and faces (cells) does an nd ...
2021年3月19日 · A 3d hypercube is a cube. It has 8 verticies and 12 edges and 6 faces. A 4d hypercube has 16 verticies and not sure how many edges or 3d faces. We can define the faces of an nd hypercube as being (n-1)d hypercubes. So the faces of a cube are squares. An nd hypercube has $2^n$ verticies.
combinatorics - How to draw the 5 dimensional hypercube graph …
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Surface Area of a Hypercube - Mathematics Stack Exchange
The only thing to remember is that we need to shrink figures symmetrically, that is the formula should be dependent not on side-length, but half of side-length (like radius for balls instead of diameter). For example, sphere volume is 43πr3 4 3 π r 3, sphere surface area is 4πr2 4 π r 2, cube volume is (2r)3 = 8r3 (2 r) 3 = 8 r 3, cube area ...
How do I figure out the features of a cube in 4 dimensions?
2015年9月24日 · Thus, we have $3 \cdot 4 = 12$ edges of the one dimensional cube. The fancy way to write this would be to say that we have $${3 \choose 1} \cdot 2^{3 - 1}$$ faces of dimension $1$ in a $3$-dimensional cube. How about writing down a two-dimensional face?
geometry - How to project 5D to 3D? - Mathematics Stack Exchange
2018年3月5日 · In this video (see also here), the author shows the projections of a pentaract (5 dimensional cube) in 3D. He explains that the tesseract (4 dimensional cube) has been projected to 3D by a stereographic projection. I totally understand that (I have done the same). But then, he explains that the pentaract has been projected to 3D by a double ...