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Questions tagged [geometry]

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

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-3
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0answers
18 views

How many more people would fit on a New York City subway car if everyone held their backpack in front of them vs. wearing it on their back? [on hold]

I'm trying to prove a point here, but probably don't have enough information. Let's assume: Average capacity per car = 200 people standing (without backpacks) Average backpack depth = 9 inches ...
2
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1answer
48 views

Is the defintion of *inertial reference frame* given by Blandford and Thorne acceptable?

Edit to add: A simple explanation of my objection to Blandford and Thorne's definition of inertial reference frame (which they use synonymously with inertial frame) is that, if I'm in free float, ...
2
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1answer
47 views

Geometrical optics problem and broader questions about the correct use of $\approx$ in physical calculations

My textbook, Fundamentals of Photonics, Third Edition, by Saleh and Teich, gives the following: This seems to be mathematically incorrect to me? Firstly, the author stated that $\phi = \psi - \...
2
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1answer
114 views

What is the length of the yarn in a ball of yarn?

The image https://commons.wikimedia.org/wiki/File:Ball_of_yarn_10.jpg shows a typical ball of yarn. Such a spherical ball of radius $R$ has a volume $4πR^3/3$. The radius of the yarn is $r$. How long ...
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0answers
22 views

If you have a cone and a ball of same radius,by how much will the ball go in by [on hold]

There is ball of Radius R and a cone of the same radius R,then how much will the ball go in by?
3
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1answer
215 views

New way to compensate for gyroscopic drift

Let us assume two points in 3D space and we only care about their orientation, no velocity, position or acceleration. Now connect those two points with a rigid body of certain length, so that the ...
0
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1answer
155 views

Can elementary particles be abstractly represented as polytopes or geometric functions?

In Quantum Field Theory, elementary particles are represented like localized oscillations (localized transverse spherical standing waves) of their underlying fields, or superpositions of their normal ...
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0answers
8 views

Calculate the changing morphology of a rubber ball

Imagine you have a rubber "bouncy ball" and you push your thumb hard into the ball. Some deformation will occur around your finger. However, the general morphology of the ball won't change in the same ...
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0answers
78 views

What is the difference between complex numbers and 2D vectors? [migrated]

This is a follow-up to a previous question regarding complex numbers. Many people there compared complex numbers to vectors, and there was disagreement about what the difference was. Some options ...
9
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3answers
427 views

Can we see the curvature of a surface?

After reading the Feynman lectures' (chapter 42, Vol.2) , it had me thinking if it is by any way possible to measure the curvature of a surface (think, surface of earth) just by observing the nature ...
1
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1answer
196 views

What is the diameter size of the umbra shadow cone of the Earth when the Moon passes through it on a lunar eclipse?

I am sure this varies given the distance from moon to earth varies, but a range would be sufficient. I am trying to explain to a flat earther how there is not a lunar eclipse every full moon. My ...
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0answers
28 views

What is meant by “neighboring points”?

I have recently been frequently encountering the phrase "neighboring points" during my studies. For example: Fermat's Principle. Optical rays travelling between two points, $A$ and $B$, follow a ...
4
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2answers
183 views

When is a circle not a circle?

Imagine a 2D uniform circular motion of constant magnitude but changing direction in an area of zero g. The forces will be equal all the way round - it will be a perfect circle. Now imagine the same ...
4
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1answer
216 views

(I-beam vs rectangular beam) Which sword blade cross section is less likely to break?

Original question Assumption: i made several swords with different cross sections (lenticular, single broad fuller as in viking swords, diamond, hollow ground diamond) the blades are made using the ...
1
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3answers
91 views

If extra dimensions are out there, why don't/can't we see them? [duplicate]

String theory proposes the existence of extra space dimensions. Very brilliant minds believe in their existence. Of course, I could appreciate that they are consequences of mathematical ...
9
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2answers
1k views

Geometrical interpretation of the Dirac equation

Is there an intuitive geometrical picture behind the Dirac equation, and the gamma matrices that it uses? I know the geometric algebra is a Clifford algebra. Can the properties of geometric algebra, ...
33
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11answers
8k views

Is the “spacetime” the same thing as the mathematical 4th dimension?

Is the "spacetime" the same thing as the mathematical 4th dimension? We often say that time is the fourth dimension, but I am wondering if it's means that time is like the fourth geometrical axis, or ...
0
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2answers
118 views

With north and south poles fixed, do all geodesics have constant $\theta$ and $\phi$?

I was going thorough reading Kolb and Turner's The Early Universe where in Section 2.2 it starts by asking the following question. For a comoving observer with coordinates $(r_0,\theta_0,\phi_0)$, ...
2
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1answer
46 views

How many images are formed when an object is placed between two plane mirrors with angle $72^\circ$?

I'm a little confused here since there are varying answers on the internet, and I cannot find any legitimate sources explaining this problem. According to what I've seen, the formula is simply $$ N = ...
0
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2answers
2k views

Making a cut trough a center of mass, can the masses of the pieces be equal?

Let's say point $P$ is the center of mass of an irregularly shaped object. If I make a straight cut trough point $P$ and split the object in two, is it possible for the two pieces to have the same ...
13
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4answers
3k 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 ...
2
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2answers
255 views

What does the $a$ stand for in this picture? (And some clarification)

(source: polygonal.de) (source: polygonal.de) $$ I_{triangle} = \frac{b^3h-b^2ha+bha^2+bh^3}{36} $$ $$ I_{total} = \sum^n_{k=1}(I_{triangle}+Md^2)_k $$ Source is here. I'm trying to understand ...
2
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1answer
285 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 ...
3
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5answers
10k views

How much of the sky is visible from a particular location?

From a particular point how much of the sky can be observed. For simplicity sake let us assume the particular point is the head of a 6 foot tall man floating in the middle of the ocean with no visible ...
2
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1answer
256 views

What are the points in spherical coordinates?

Let's use the spherical coordinates so that $\vec P=(r, \theta, \phi)$. In this context i've read that it's possible to write $$\vec P'=\vec P + d\theta\ \vec e_\theta+d\phi\ \vec e_\phi+dr\ \vec e_r$$...
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1answer
5k views

de Laval nozzle geometry

After doing some research I was not able to find any information on the geometry of the de Laval nozzle. Are there some kind of ratios that the different sections' radii and lengths have to be in? ...
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3answers
59 views

Does temperature coefficient of resistance depend on geometry?

By temperature coefficient of resistance of a material about a reference point $T_0$, I mean $${1\over R(T_0)} \left.{dR\over dT}\right|_{T_0}.$$ All the sources (that I’ve seen) that quote this ...
3
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1answer
54 views

What's the meaning of the coordinates if we use a polar coordinate system?

In general, the coordinates of a vector are defined as the projections of it onto the coordinate axis. Moreover, in a polar coordinate system, the basis vectors $\hat e_\phi$, $\hat e_r$ depend on the ...
1
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2answers
585 views

Why are many things in the universe round?

Take a walk outside and you'll realise many things are round. Wheels are round, a cup is round and even that home button on your iPhone is round. But that's all man made. In nature, there are many ...
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0answers
31 views

Computation with bispinors for a compatible pair of pure spinors in N=1 supersymmetric vacua compactified down to 4-dimension

I ask this question basically because I need help, just an hint, for a computation with bispinors. The background is string theory / supergravity, where many data of a supersymmetric vacuum can be ...
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4answers
104 views

3 Dimensional Law of Cosines? Magnetic Vector Potential Problem

I am working on a problem similar to one in my textbook - however, I am having an issue understanding the example. Can someone explain the formulas from this picture? I am confused about using the law ...
1
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1answer
206 views

Deformation of a self gravitating sphere from two forces

I have a fluid sphere (say a gas or a liquid of uniform density, under its own gravity) on which forces is applied to its surface. I would like to find its approximate shape (most probably an oblate ...
1
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1answer
41 views

Intuitive understanding of angular momentum in cartesian coordinates

If a point-mass body is moving in a plane $z=0$, its angular momentum can be taken to be a scalar, and from the vector product formulas (assuming $m=1$ as I'm only interested in geometry), its value ...
1
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1answer
80 views

Why do headlights through a window move around a room?

As I lay in bed this evening a few cars have passed by and my blinds are down. As they come down the street, you can see a sliver of light on the wall on the side of the room that is in the direction ...
0
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4answers
226 views

Is a shadow 2D?

I had always thought anything below third dimensions couldn't exist in our 3rd-dimensional world. Correct me if I'm wrong but anything 0d 1d or 2d is massless and also can't have energy so it just can'...
0
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2answers
168 views

Centre of gravity and centroid

Are the geometric centre & centre of gravity of a right angled triangle at different coordinates ?
0
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2answers
55 views

Are there two ways of representing a vector i.e., parrallelogram and resolution?

the question was: The component of a vector is (a) Always less than its magnitude (b) Always greater than its magnitude (c) Always equal to its magnitude (d) None of these ...
2
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4answers
208 views

Different expressions for distance & displacement : $\int$$d$$|\vec r|$, $\int$$|$$d$$\vec r$|, and $|$$\int$$d$$\vec r|$

I came across these expressions in my book. And the book says that all these are different from each other. The expressions are : $\int$$d$$|\vec r|$, $\int$$|$$d$$\vec r$|, and $|$$\int$$d$$\vec r|$ ...
3
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1answer
95 views

Why does a wormhole have this metric?

I asked this (or something similar) within another question and was asked to post it separately, so here goes: The metric for flat Minkowski space is: $$ds^2 = -dt^2 +dr^2 +r^2(d\theta^2+d\phi^2\sin^...
2
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1answer
64 views

What's the problem with Euclidean geometry for astronomical phenomena?

This passage from John Pierce, An Introduction to Information Theory: "also note that while Euclidean geometry is a mathematical theory which serves surveyors and navigators admirably in their ...
0
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1answer
95 views

Weird assumption in a paper to prove equation [closed]

Let $M_k$ and $M_{k+1}$ be two successive positions. Supposing the road is perfectly planar and horizontal, as the motion is locally circular, we have: Where $\Delta$ is the length of the circular ...
0
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0answers
32 views

Is every observer equidistant in all directions from the point of origin of the universe? [duplicate]

I am interested in the origin and present structures of the dimensions of space and time. I do not think space/time can be correctly described by an ordered set of scalars: (x,y,z,t). So. If every ...
1
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0answers
30 views

Square gears pitch curve relationships [closed]

I am trying to design square gearset using MATLAB program. I have designed several ones (elliptical, eccentric, spiral, circular ....etc). But when I came to the square gears, I needed the ...
3
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1answer
44 views

Are special conformal transformations continuous?

My understanding of special conformal transformations (SCTs) is fairly limited, but I believe that they are composed of an inversion, a translation and another inversion. Since inversions are discrete ...
1
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2answers
2k views

Moment of Inertia of Torus

I was trying to find the moment of inertia of the Torus with respect to the axis in the center perpendicular to the bigger circle's plane; see image: So: the radius of the magenta circle is $\rho$, ...
1
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1answer
60 views

Why do the rail tracks seem to converge and vanish? [duplicate]

Why do railway tracks seem to converge at a far away point? Can this phenomenon occur with a very far away tall wall (considering I stand on a flat plane, not the curved surface of earth). Isn't ...
5
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2answers
396 views

Combining rotations for orbital and rotational motion of a planet

If I have a planet orbiting the Sun (assuming circular orbit) at angular velocity $\Omega$ and rotating about its axis at $\omega$. I also have a normal to the surface of the planet $\vec{n}_{\rm surf}...
0
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1answer
96 views

How did German radio beams reach distant English cities during WWII? [closed]

During WWII, the Germans were using radio beacons (the "Knickebein" system) to guide their bombers into English territory. They set up two beacons, one in Kleve, a city in West Germany, and one at ...
2
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1answer
347 views

Sound - for purposes of vibration

What is the best way to distribute noise from more than one source (I'm envisioning a system with many), within a dome, with the ground as its primary target, at optimal frequencies and volumes to ...
1
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1answer
86 views

Lorentz Factor from Minkowski's Original Paper 'Space and Time'

Consider the following figure: Minkowski, in his paper 'Space and Time', derives the Lorentz factor $\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$ from considerations of this figure. He ...