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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18 views

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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1answer
36 views

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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28 views

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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3answers
84 views

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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30 views

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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53 views

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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40 views

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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2answers
238 views

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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1answer
38 views

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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1answer
40 views

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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1answer
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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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2answers
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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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1answer
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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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1answer
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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 ...
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1answer
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How to express in terms of spacetime intervals whether two participants in a flat region were at rest to each other

Given a flat region of spacetime as set $\mathcal S$ of events together with values of spacetime intervals (up to a common non-zero constant) for each pair of events, $s^2 : \mathcal S \times \mathcal ...
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1answer
38 views

How is hemispherical shell any different from a semi-disc in terms of center of mass? [closed]

If we shift all the rings that make up the hemisphere parallel towards the center then it will build up two semi-disc .. But we know that We can also explain it by saying that if we take the shadow ...
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1answer
39 views

Slackline tangling

This question is about random formation of knots in a systematically tied rope. I will give some background, hope that does not make it off-topic. In climbing (and sailing) one has to store very long ...
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1answer
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Component of Component of a vector [duplicate]

NOTE : By perpendicular component of $\vec{F}$, I mean a vector which is a component of $\vec{F}$, but perpendicular to it. In the image above, the red vectors are a possible set of rectangular ...
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How to interpret the units of the dot or cross product of two vectors?

Suppose I have two vectors $a=\left(1,2,3\right)$ and $b=\left(4,5,6\right)$, both in meters. If I take their dot product with the algebraic definition, I get this: $$a \cdot b = 1\mathrm m \cdot 4\...
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1answer
50 views

Satellite and gravitational acceleration

According to $0.5gt^2$ object will fall 5m in first second. Earth curve is 5m for 8km So if we can project object at 8000 m/s speed object will never fall into ground. Above scenario is correct ...
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1answer
36 views

Center of mass/centroid changes between 2d and 3d?

Unless I completely botched the calculation, I noticed something strange: if you find the centroid of a 2d curve, and then revolve the curve around its axis then find the center of mass, the CM is ...
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1answer
56 views

How does one calculate how big something has to be, to be seen at a given distance? [closed]

Ignoring curvature of the Earth. How do I calculate the size an object would need to be in order to appear to be approx 1cm tall at a given distance?
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1answer
46 views

Small enough planet to notice rounding

This is my first question on Physics StackExchange, so bear with me. I am wondering. How dense would a planet need to be for a human to notice the fact that the planet is not flat, but round, by ...
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2answers
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Find the relation between length of pulley and strings [closed]

A pulley is pulled with external force $F$. $x$ and $y$ denote the displacement of two ends of strings of the pulley and $z$ is the displacement of the pulley. Prove That $$z = \dfrac{x+y}{2}$$...
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2answers
153 views

Is curvature space-time has impact on the object geometry

When we have e.g. metallic cube of dimensions 1x1x1m and we put it on the space without gravitational force the cube has equal 1x1x1m and we can use Euclidean geometry. But when this cube move on ...
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1answer
55 views

Does the expansion of the Universe into a higher dimensional space imply that 4-D objects are real?

It is my understanding that objects in the Universe are not just getting farther apart but space itself is expanding and so in some real sense, higher-dimensional geometry is "real" -- if so, on a ...
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2answers
71 views

Perspective Redux (why objects seem smaller as the distance increases) [duplicate]

Last time I brought this up, the best answer featured an image that looked something like this: The argument here is that as the distance increases between the eye and the object, the angle gets ...
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1answer
69 views

Understanding Euler's rotation theorem

According to Euler's rotation theorem, simultaneous rotation along a number of stationary axes at the same time is impossible. If two rotations are forced at the same time, a new axis of rotation will ...
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9answers
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Why do objects appear smaller when viewed from a distance? [duplicate]

Yes, I know all about perspective (I'm an artist). I even have some basic knowledge of descriptive geometry. I know how it works. My question is more about why it works. I have a sneaking suspicion ...
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1answer
47 views

Representing 1+1 Minkowski space as a surface in 3D Euclidean space

In 1+1 Minkowski space the distance between two points is given by$$ (x_1 -x_2)^2 -(t_1 - t_2)^2.$$ This is different from the Euclidean distance. But is it possible to come up with a 2D surface ...
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0answers
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Does Earth eclipse the Sun at the L2 Lagrange point?

Is Earth's diameter large enough to eclipse the sun at the L2 Lagrange point? Or does the sun shine around the edges of the earth? I understand the useful area of the L2 Lagrange point is somewhat ...
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1answer
47 views

Center of mass of an arc

A very thin tube shaped like a quarter of a toroid has one end attached to the origin $(0,0,0)$ and the other end at $(R,0,R)$. Determine its center of mass. So obviously $y_G = 0$. Using Pappus ...
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2answers
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The Physical Basis of Our Assumptions about Physical Space

Let $\mathcal{S}$ represent the set of all points in physical space. Using measuring rods and assuming our use of them does not depend on time, we can establish a one-to-one correspondence between $\...
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View factor of two parallel coaxial *rectangular* plates

I've found a lot of tables and resources that list view factors (VF) for various geometrical configurations, but I couldn't find a single one that has the VF for two parallel coaxial rectangular ...
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26 views

How to calculate apex angle of sun shining on the Earth

I'm trying to compare the brightness of various LEDs to the average brightness of natural daylight. LEDs are rated in terms of candelas whereas the Sun is measured in terms of lumens, so I need to ...
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2answers
120 views

Does gravity have two directions?

Imagine a particle that interacts strongly with gravity, but not with any of the other forces, and does not interact with normal matter (this may be analogous to the description of dark matter, I'm ...
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Derived Geometry and Deformation Quantization

Can anyone please explain to me in layman' terms what derived geometry deals with and what deformation Quantization is? I have only a good understanding of Relativity,Classical Mechanics.
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4answers
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Why is the Pythagorean Theorem used for error calculation? [duplicate]

They say that if $A = X \times Y$, with $X$ statistically independent of $Y$, then $$\frac{\Delta{A}}{A}=\sqrt{ \left(\frac{\Delta{X}}{X}\right)^2 + \left(\frac{\Delta{Y}}{Y}\right)^2 }$$ I can't ...
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2answers
126 views

Can an angle be defined as a vector?

In Classical Mechanics angular velocity, angular acceleration, torque and angular momentum can be defined as vectors with clear advantages such as the possibility to use vector product to simplify ...