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Pyramid (so square based?) You would see a 5 sided square-- meaning the pyramid would have 5 faces and the base still would have 4 sides(square) yet somehow when you look at it every face lands on a side it's quite confusing to look at let alone make sense of. That would be my most simple answer to give since I see lots of long complicated answers I figure I ...


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A straight line in a dimension 8 (say Euclidean) space is a one dimensional object embedded in a 8 dimensional space. To look at it means to project it onto some 2-dimensional surface. Think about moving a camera around in 3-space, your camera captures 3 dimensional objects onto a screen or a photograph which is 2 dimensional, this is what I mean by looking ...


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A straight line also looks like a line in three dimensions; what's new in three dimensions is the ability to build intersecting planes, from which you can construct skew lines (nonintersecting, nonparallel) and three-dimensional objects. In four dimensions you can construct hypersolids. (I'm not sure how much attention the hypercube/tessaract gets outside of ...


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You're asking two separate questions. To take your second question first, the existance of seven extra spacelike dimensions is a requirement for the consistency of string theory and we have no experimental evidence that extra dimensions exist or that string theory is a good description of reality. So it's impossible to make any definitive comment about why ...


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Reynold's number is defined to be: $$ \text{Re} = \frac{ v D }{ \nu } $$ where $v$ is the characteristic velocity for the flow, $D$ is a characteristic size and $\nu$ is the kinematic viscosity. Now, why should we care? Why is Reynold's number important? Well, the first thing to realize is that the Reynolds number is a dimensionless number. This means ...


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Why time is considered to be a dimension? Because, to the extent of the empirical evidence, relatively moving inertial observers are related by the Lorentz transformation. But, the Lorentz transformation mixes time and space coordinates in a particular way. If time were not a dimension, if time were just a universal parameter, this mixing would not be ...


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I think you should understand the passage a bit more abstractly: Take the space $\mathbb{R}$. It's obviously one-dimensional. Now, consider the space $\mathbb{R}\times\mathbb{R} = \mathbb{R}^2$, the vector space over $\mathbb{R}$ with two dimensions. You have thus created a two-dimensional object from a one-dimensional one. Let us now construct the book: ...


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It seems that this question is asked because of difficulties in trying to visualize higher dimensions. Fig.1: The full manifold is here $\mathbb{R}^2\times S^2$. I) Let us therefore for simplicity assume that the physical universe is just a 2D cylinder$^\dagger$ surface $\mathbb{R}\times S^1$. Imagine that there are only one large (uncompact) ...


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Let me try to rephrase what you're asking. Suppose we have the usual spatial dimensions $x$, $y$ and $z$, and a compact spatial dimension $w$. Then can we have two particles simultaneously at positions: $$ P_1 = (x, y, z, w) $$ and $$ P_2 = (x, y, z, w + \delta w) $$ In other words the particles are at exactly the same position in the normal coordinates ...



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