# Tagged Questions

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

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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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### Generators of cubic group: Euler angles

I am trying to build numerically all members of the cubic group in the representation of Wigner D matrices. Angular-momentum quantum number may be small, e.g. 2, so I use the formula stated e.g. at ...
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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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### Geometric meaning of negative triple product [migrated]

Create a tetrahedron with corners $A=(1,2,4)$, $B = (1,0,2)$, $C = (2,1,3)$ and $D = (4,1,1)$. Determine the angle $\alpha$ between the edge $AB$ and the side $BCD$. The first step I make is ...
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### 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 ...
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### 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 ...
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### 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, ...
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### Feynman lectures, Volume I, chapter 13-4 [migrated]

While reading Feynman lectures on Physics, volume I, Chapter 13-4, I found following assumption, which I don't understand: Then, since $r^2 = \rho^2 + a^2$, $\rho\,d\rho = r\,dr$. Therefore ... ...
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### 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 ...
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### 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 ...
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### 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", ...
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### 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 ...
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### Determining Height of Platform on Fulcrum

Consider this scenario: We have a platform resting on a fulcrum. The platform's tilt is controlled by a motor attached to 2 levers: Is the link between the height of the top of the lever ...
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### The relationship between abstract geometrical concepts and reality? [closed]

In pure geometry points have no parts, lines no breadth and surfaces no thickness, geometrical figures can be exactly congruent. But how do these concepts relate to the physical world. What is the ...
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### Defining a room that is equally lit at every point

Imagine you were in a room designed such that no matter where in the room you stand, a sphere of volume 1 liter held at 2 meters above the ground would be exposed to the same amount of light. How ...
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### 3D donuts and the centre of a black hole [closed]

I have been trying to imagine ways to visualise the gravitational field of the earth... It's near zero at the outer edges of the atmosphere, strong at sea level, strongest at the quarter point, then ...
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### 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 ...
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### Relative motion of an arbitrary volume of space ( is space static or dynamic?) [closed]

Do physicists consider space as being "static" or "dynamic" ? Hi I asked a question about whether space can move, and from the answer, I realized I was not precise enough and did not actually ask ...
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### Angular current in torus

I'm trying to find the magnetic field due to a torus anywhere in space. I'm approximating it as a circular current loop. What I'm having a hard time with is the current in the theta direction, that ...
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### Can a die be made unfair without changing the center of mass or the exterior?

This question came from trying to design some 3d printed dnd dice. I think it's possible to make a die unfair without changing the center of mass or affecting the exterior shape*, but I'm not sure ...
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### Proving that the Center of Mass of a solid sphere is at the origin [closed]

For my own knowledge and to understand why. I am trying to convince myself that the center of mass for a rigid solid sphere is at the origin (0,0,0). I begin with the basic definition of CM ...
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### New direction vector after collision of spheres [closed]

I have a volume in 3-space in which random spheres are spawned in motion. They have the following attributes to them: position known (in three axes) a direction vector (in three axes) a scalar speed ...
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### How small would the patch of sun be that delivers heat to the earth?

The sun, being a ball, projects its EM radiation and light in all directions. We earthlings only receive a light from a portion of the sun, not all of it. What size is this patch of the sun's surface ...
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### Can quantum mechanics, general relativity and all physical theories be reduced to geometry? [duplicate]

I was told by my, perhaps ignorant (that is for you to decide), teacher that "all physical theories can be reduced to geometry in the manner of Newton's Principia/Euclid's Elements, however, due to ...
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### Why sphere minimizes surface area for a given volume?

I was studying surface tension recently. Rain drops or bubbles of any kind which form are always of a spherical shape. This is because the liquid tries to minimize the surface area as the molecules ...
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### Can 3 objects be collinear?

Suppose there are 3 objects floating in some space, without anything else besides this 3 objects. Is there any way for them to end up collinear at any given moment (assuming they start at completely ...
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### How do quantum particles interact with each other? [closed]

Does infinite expansion of particles become finite when the smallest stuff that makes up matter interact with each other? Would then those particles be in the form of shapes,such as platonic solids ...
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### How can we see the moon while it's between the Earth and the Sun?

I know this sounds like (and probably is) a stupid question, but I can't figure it out. As far as I know, the crescent shape of the moon is when the moon is on the sunny side of the Earth, but that ...
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### Simple Stern-Gerlach Apparatus Orientation

I have been reading Townsend(2012)A Modern Approach to Quantum Mechanics. In the first chapter, he introduces the idea of intrinsic spin angular momentum, and some of its strange quantum properties ...
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### Physics related derivation of equation of cycloid

So I was trying to find the path traversed by a point on the rim of a rolling disc. I eventually landed up at an equation but when I went to check it out in the internet, I couldn't find any similar ...
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### The dual of a surface element in 4-space

In reading the classic text, "The Classical Theory of Fields", Third Edition, by Landau and Lifschitz, I found an "obvious" statement not so obvious to me. It is on p.19, the statement of the ...
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### Can space move? [closed]

I have some questions; I hope you don't mind: $\bullet$ If the space between two distance galaxies is increasing, then is the volumes of space in which the galaxies find themselves also moving apart? ...
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### Why is $\pi$ the value it is? [closed]

Why is the value of $\pi$ 3.141592...(etc.)? Is it a fundamental property of our universe? Or does it follow from our definition of what a circle is, or does it otherwise follow from the way we ...
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### 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. ...
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### What does the $a$ stand for in this picture? (And some clarification)

$$I_{triangle} = \frac{b^3h-b^2ha+bha^2+bh^3}{36}$$ $$I_{total} = \sum^n_{k=1}(I_{triangle}+Md^2)_k$$ Source is here. I'm trying to understand the mass moment of inertia in order to create a ...
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### What is the difference between a hollow (sphere/cylinder) and a shell (cylinder/sphere)? [closed]

First of all, it was hard to "tag" this question ! Anyways, I see some contradictions in what a shell or a hollow cylinder is in some sources in the internet based on some figures they show. I ...
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### Given a dimension of a known object in the image, how can we calculate the dimension of other objects in the same image ?

The question considers a very specific scenario in which we have an image with let us say, two rectangle objects. We know width and height of one object. How can we calculate the dimensions of the ...
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### A teaser on center of mass of right circular cone?

How can a distinction be made between the centre of mass of a right circular cone As a uniform solid ($\frac{h}{4}$ from base, where is $h$ is height) and That composed of infinitesimally small ...
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### Absolute direction in space [closed]

Rotation, from my understanding, is basically the "exchanging of different spatial dimensions with eachother", with $x^2+y^2=d^2$ being the "relationship" between any two spatial dimensions, aka. if ...
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### Is there a geometric interpretation of the spacetime interval?

In Euclidean space, the invariant $s^2 = x^2+ y^2+ z^2$ is equal to the length square of the position vector $r$. This is easily understood and can be represented geometrically in a graph. On the ...
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### Center of mass (COM) of a uniform quarter disk [closed]

I was trying to calculate the coordinates of the COM for a uniform quarter disk. By symmetry, it must lie on the angular bisector of the central angle. Also, $A=\frac{\pi R^2}{4}$, thus ...
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### What is the meaning of “a straight line”? [duplicate]

The book "The Dancing Wu Li Masters" page 189 talking about General Relativity says "A geodesic is not always a straight line". Is that true? What is a definition of "straight line" that makes sense ...
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### Investigating volume of a crater

I determined the shape of the crater to be a spherical cap. According to this website, http://mathforum.org/library/drmath/view/55253.html , its formula is described as V_{cap} = \frac{1}{6} \pi h ...
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### Land proportions in NASA blue marble photographs

What is the explanation for the apparent size difference of North America in these two photos from NASA? Image source Image source
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### How big are clouds? [closed]

How big are clouds? When I look up into the sky I have no frame of reference, so I don't know if they are 200 feet or 2 miles across. When I am in a plane looking out at a cloud, I try to use the wing ...
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### How is Chasles' Theorem 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 ...
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### Order of magnitude for the range of vision

Let's say you're in the middle of a desert, with nothing but sand. Let's also assume that you have a 20/20 vision. When you're just looking there's a point that your eye can't reach name it $M$ and ...
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### Centre of gravity vs centre of mass for a pyramid mounted on a cube, all sides of length $l$ [duplicate]

A uniform solid body is constructed using a square-based pyramid mounted on a cube. If each edge of the solid has length $l$ show that the centre of gravity of the body lies within the cube is, \$\frac ...