All Questions
Tagged with dimensional-analysis dimension-theory-analysis
11
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What is the dimension of this set of points?
The following set of points in $\mathbb{R}^n$ is full-dimensional ($n$-dimensional):
$$\{(x_1,\ldots,x_n)| 0\leq x_i \leq 1 \text{ for all }i\in[n] \}$$
What is the dimension of the following set - is ...
- 10.8k
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How to find the box counting dimension of line segment [0,1]?
I uploaded this question and no one has answered because there were some flaws in the question but I have the text now. Please can some one explain how we arrive on example of line segment to have a ...
- 41
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Can you mix units of $t$ and $t^2$ when constructing a shape?
Let's say I have a length (possibly a radius), we'll call it $y$ and is of unit $t$. My data suggests to me that the distance around this shape (possibly a circumference), is $y^2$, which means the ...
- 233
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Fitting a line through a complex 2D shape, use of multi-dimensional projection?
I am working with a complex 2-dimensional shape (similar to this image), and would like to pass a single, continuous line through it to aid future analyses. I have distinct data points on each pixel ...
- 133
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Is there any software that can exhibit 4th dimensional objects in a 4D space?
I want to model an object in 4D. Just like the 3D simulation softwares (like Autodesk Maya, 3D Studio Max, etc.) but in 4D.
Please keep in mind that I'm looking for a computer program that can ...
- 111
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59
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Simulating 4D on a 3D mean
Why if we can simulate 3D on a 2D mean, why isn't possible to simulate 4D on a 3D mean (real world)? Has someone tried?
- 163
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How can one do dimensional analysis when units are not known?
In the sciences, we can do dimensional analysis and unit checks to verify whether or not the LHS and the RHS have the same units. If we have the following function:$$y=f(x)=x^{2}$$
what ensures the ...
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Obtaining a solution space to an inverse kinematics problem (mapping a higher dimensional space onto a lower one)
I have a 15 dimensional space (corresponding to 15 joints of a robot, 5 joints for each of two legs, and another 5 joints for the right arm). I'll call this space A. Bear in mind that each of the 15 ...
- 111
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Hausdorff dimension of F and f(F)
We have F being a subset of R, [-1,1], while f:R->R, where f(x)=x^2.
What's the Hausdorff dimension of F and f(F)? I think the dim(F)=2(length) and dim(f(F))=1, is it correct? Thanks,
- 429
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Integral over Fractals with respect to fractal dimension
I understand that there is type of integral with respect to measures that can return values when evaluated over an integral. But is there an Integral that returns d dimensional volume where d is the ...
- 8,361
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Is a Möbius Strip in > 4 dimensions impossible?
I seem to remember reading, on a plaque in the math building at Penn State, that Möbius Strips are only possible in 3 and 4 dimensions. In higher dimensional spaces, a Möbius strip will use the extra ...
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