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

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5
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2answers
392 views

How is Chasles' Theorem, that any rigid displacement can be produced by translating along a line and then rotating about the same line, true?

Chasles' Theorem in its strong form says: The most general rigid body displacement can be produced by a translation along a line (called its screw axis) followed (or preceded) by a rotation about ...
9
votes
3answers
507 views

What is the exact meaning of homogeneity in cosmology?

I understand that, in general, homogeneity is the physical attribute of being uniform in composition (" of the same form at every point"), but I'm slightly confused when it is used in cosmology as ...
2
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1answer
33 views

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 ...
0
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0answers
37 views

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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0answers
12 views

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 ...
5
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2answers
96 views

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 ...
2
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2answers
146 views

How many are the points which are $n$th nearest to a certain point in a hexagonal lattice

Suppose there are infinite points arranged as hexagonal lattice. The question is the one as the title. First we choose a point called $A$. Then when we count the $n$th nearest points to $A$, what ...
3
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1answer
56 views

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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3answers
118 views

How to find the center of rotation? (2D)

First off, I'm assuming that a free floating polygon doesn't always rotate around its center of mass unless the net force is zero (based on the points below). If this isn't correct please tell me. ...
0
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1answer
41 views

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 ...
1
vote
1answer
16 views

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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9answers
2k views

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 ...
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1answer
153 views

How do you compute for the center of a rotation of a bicycle?

I know how to find the center of a rotation, like where you connect the side and make bisector with the help of your compass. But in a situation like this how do I get the $a_2$? I'm doing an advance ...
1
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1answer
34 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 ...
1
vote
1answer
159 views

Structure factor of crystals (X-ray crystallography)

How can one prove that the degree of each node in a distance graph must be at least four in order to obtain a unique solution to an exact distance geometry problem with sparse distance data? The ...
3
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2answers
517 views

Finding the illuminance from a triangular light source

Since most light sources in games are point-like, it's pretty difficult to approximate area light sources with point sources. As triangles are a universal form to represent 3D models (thus area light ...
3
votes
1answer
30 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 ...
1
vote
1answer
35 views

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 ...
24
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6answers
63k views

What is the physical significance of dot & cross product of vectors? Why is division not defined for vectors?

I get the physical significance of vector addition & subtraction. But I don't understand what do dot & cross products mean? More specifically, why is it that dot product of vectors ...
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2answers
1k views

What is the physical meaning of a dot product and a cross product of vectors? [duplicate]

My teacher told me that Vectors are quantities that behave like Displacements. Seen this way, the triangle law of vector addition simply means that to reach point C from point A, going from A to B ...
1
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1answer
30 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 ...
2
votes
1answer
49 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 ...
3
votes
1answer
36 views

Find the relation between length of pulley and strings

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 = ...
1
vote
1answer
54 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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vote
1answer
45 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 ...
3
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2answers
145 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
379 views

Null lines and degenerate plane

Can anyone explain me what null lines are and degenerate plane? I don't know anything about it, I don't have physics background and I am a mathematics student and please tell me if there is any good ...
0
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1answer
49 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 ...
0
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2answers
64 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 ...
1
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1answer
60 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 ...
16
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9answers
4k views

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 ...
1
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2answers
56 views

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 ...
1
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1answer
47 views

Coulomb collision

I was reading an article by N. Bohr and came upon the following problem (the following wording is actually taken from a book by Thompson - Conduction of Electricity Through Gases): Let $M_1, M_2$ ...
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0answers
50 views

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 ...
1
vote
1answer
44 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 ...
1
vote
1answer
41 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 ...
0
votes
0answers
22 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 ...
0
votes
0answers
28 views

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 ...
0
votes
2answers
114 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 ...
2
votes
4answers
110 views

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 ...
3
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0answers
40 views

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.
2
votes
2answers
106 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 ...
-1
votes
1answer
67 views

If the Earth were a pool ball, could I feel mountains? [closed]

If the earth (12,742 km diameter) were scaled down to the size of a pool ball (61mm diameter), the mountain ranges would still exist, obviously. But would a typical human be able to feel those ...
5
votes
3answers
276 views

What is the difference between the shapes of molecules with different isotopes

I'll explain my question on example of water molecule. Let us have three water molecules: normal water $H_2 O$, heavy water $D_2 O$ and semiheavy water $HDO$. Is there any difference between the ...
-1
votes
1answer
59 views

Finding angle between two displacements [closed]

Consider two displacements, one of magnitude 6 m and another of magnitude 8 m. What angle between the directions of this two displacements give a resultant displacement of magnitude (a) 14 m, (b) 2 m, ...
4
votes
4answers
238 views

Bicycle counter-intuitive: in which direction it will move? [duplicate]

I saw this puzzle in a local newspaper: Consider a normal bicycle set to stand in its upright position, and its pedal is set to the position as shown in this figure. One man slightly hold the ...
2
votes
0answers
51 views

Terminology - optical (visual) properties of a structure

I am trying to understand few terminological problems that I encounter. Without knowing keywords it is hard to perform search for literature or publications in the area. The area relates to the ...
2
votes
0answers
38 views

The Ehrenfest Paradox and Euclidian Assumptions [duplicate]

As a result of the Ehrenfest Paradox, the geometry of a rotating disc is non-Euclidean. However, while reaching this conclusion, we assumed that "the radius doesn't undergo Lorentz contraction", ...
0
votes
1answer
369 views

Area moment of inertia of regular $n$-gons over polygon center $O$

Is it possible to consider the regular polygons ($n$-gons) as deformed circles and use a pseudo-polar coordinate system to calculate their moment of inertia over its center $O$. Inasmuch as I know (I ...
3
votes
0answers
32 views

Snyder's Lorentz invariant discrete space-time

Can theories which say space-time is fundamentally discrete be compatible with Lorentz invariance? And if the answer is yes, in what sense is space-time no longer continuous? I'm sure this has been ...