# Tagged Questions

To be used for questions on geometry closely pertaining to physics. Includes differential geometry and euclidean geometry.

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### Why do we have perspective in space?

In the euklide space there is nothing like perspective but in vision there is something like perspective.
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### Examples of multiply-connected compact configuration spaces

I'm a looking for examples of dynamical systems that have multiply-connected compact configuration spaces. Since I'm not a 100% sure about the correct terminology for the systems (I am sure about the ...
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### How to verify that distance in parsecs to the closest star agrees with the angle in arc seconds when the Earth moves a distance of half a year? [on hold]

The question is this exactly: What is the distance to the nearest star in parsecs? What angle does this star subtend to the Earth when the Earth has moved a distance of $2 AU$ from one side of the sun ...
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### What is the difference between intrinsic and extrinsic curvature?

In general relativity, energy bends spacetime. However, this doesn't mean that a fifth dimension for spacetime to "bend into" exists." That is, spacetime isn't embedded in a higher dimensional space, ...
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### What enclosed geometry amplifies sound the most?

I am going to build a record player. It will read sound electronically but I also want it to be able to project sound mechanically, like a classic record player. So if sound enters a tube, can you ...
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### What is the geometric explanation for why the interior angles of a triangle sum to 180 degrees in both Euclidean space and Minkowski spacetime?

Four-dimensional Euclidean space has the same topology and affine structure as Minkowski spacetime, though the two have different metric structures. Given that the interior angles of a triangle ...
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### Derive equation for shear modulus $G=E/(1+2v)$

Shear modulus, G Young's modulus, E and Poisson's ratio, v: $G=E/(1+2v)$ I have always wondered how this relation is derived, but have never found a derivation that I could follow online. I assume ...
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### What is the Direction of area vector?

In case of closed surfaces the area vector is directed outwards the surface. But what is the direction of the area vector in case of an open surface e.g. A thin lamina type of surface. Does it depend ...
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### How do we measure curvature of space? [duplicate]

I know according to general relativity, space-time is curved near mass. But I have also read that at large distances space can be curved too, and that Gauss was the first one to measure it. My ...
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### How do I draw the Minkowski diagram of a event in two inertial systems when t=t'=0?

An Introduction to Mechanics" by David Kleppner & Robert Kolenkow, 1st Edition, 12.1 Assume that v= 0.6c . Find the coordinates in S' of the following events: a). x=4 [m], t= 0[s] b). x=4 [m], ...
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### Multidimensional Area and Volume

In 3D the volume is $xyz$, the product of three coordinates. But in $N$ dimension ,how to define area and volume?
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### Difference between space of reference and system of coordinates

In the book "The meaning of the relativity" by A. Einstein, it is referring to two different concepts: space of reference and system of coordinates. What it is the difference? It says: "we ...
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### Coordinate Equation of a curve which bends all the parallel incoming rays from infinity towards a single point

How should i proceed on to find the coordinate equation of a curve such that it bends all the parallel rays coming from infinity towards a single point. Yes I know that it would be a 2nd degree ...
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### Calculating the Diameter of Jupiter through Image [closed]

I was trying to calculate the diameter of Jupiter from a picture I took of it. Here's the information I was able to get that I needed to calculate the diameter: Focal Length of Telescope: 1.2 m ...
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### Distance and Speed

When I look up in the sky and I see a plane moving and it's further away why does it seem to move so slow compared if a flock of geese flies over at same time and seems to travel faster?
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### Watching Airplanes Fly Toward You

Recently, I was enjoying the stars on a cool summer night and saw an airplane flying toward me from the distance. I observed its path as it started out as a small dot in the distance until it flew ...
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### Area moment of inertia about the y-axis for a triangle [closed]

I have a triangle which I have divided into two smaller triangles. Now I'd like to compute the area moment of inertia about the y-axis for the blue triangle. I've set the origin in the bottom between ...
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### Calculating the Velocity of an object far far away

I saw a satellite the other day, it moved very fast through the night sky. Now I know it took around 110 seconds for it to fully travel out of the night sky(out of my visual bounds assuming, that I'...
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### Area as a Vector [closed]

Why can we take area as a vector? And say if we take it as a vector why not on the plane why only perpendicular? What is positive or negative area or what the area has to do with direction?
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### Is there a 3D analogue of angle?

A one-dimensional angle is a wedge, almost like a slice of pizza. A two-dimensional angle is an angle squared, like the cone of light produced by a flashlight. This is called a solid angle. Is ...
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### What determines the sign of phase dislocations?

I am studying the nonlinear Schrodinger equation $$A_t+iA_{xx}+i|A|^2A=0$$ for $A=ae^{i\theta}$ a complex valued function, with $a,\theta$ real. I am trying to figure out what sets the signs of the ...
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### Stable Sides of Polygon Objects

I have a physics question for you. Let us say a polygon shaped object is stable on a side when the center of mass "falls" inside the base. Is it possible in 2D to build an object that is unstable on ...
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### How is the dot product a generalization of multiplication?

I've seen an interesting explanation for lots of what I previously thought were unmotivated definitions in Newtonian mechanics, namely that power is always defined as effort times flow. But when ...
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### How could the universe be hyperbolic if hyperbolic space isn't symmetrical?

In the 2-D projections of the shape of the universe shown here, we see that the flat universe and the spherical universe are perfectly symmetrical, so any triangle drawn anywhere on them will be the ...
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### How can a Satellite's position/orbit be calculated using only range measurements from ground stations?

This task is often done in a process known as Satellite Laser Ranging (SLR). SLR stations (of known coordinates) track satellites, recording range measurements to the satellite at known times. I would ...