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

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4 views

Gaze tracking with the pupil-glint response how does the geometry work?

I am struggling to understand the geometry behind the pupil glint response (see above) (With only one light source). I understand that you use the glint to find the corneal centre (Centre of corneal ...
0
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1answer
47 views

Do lower dimensional objects actually exist? [duplicate]

Take for instance a arbitrarily chosen 2-dimensional rectangle, having a length of $x$, a width of $y$ and height of 0. (Or take for instance a 1-dimensional line. Or take for instance a 0-dimensional ...
-2
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0answers
20 views

Calculating errors?

Hollow cylinder of length l, inner and outer radii r1= 2.5+-0.3mm, r2= 5.5+-0.3mm, density= 7.88g/cm^(3), mass density= p, mass= (pi)xpxlx(r2^(2)-r1^(2)). What is the mass?
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0answers
109 views

What is the fourth dimension of a Tesseract? [migrated]

Is the fourth dimension of the Tesseract time? That is why it is represented as a moving 3D structure on Wikipedia? I am asking because I have trouble understanding what it is.
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2answers
37 views

How would the representation of a circle in 4 dimensions? [closed]

We know that the representation of a square in three dimensions is a cube, and in four dimensions is a tessaract or, hyper cube. With this, How would be the representation of a circle in four ...
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1answer
26 views

In layman's terms, why would frame dragging affect precession of nearby object?

My question is really about the gravitomagnetic frame-dragging and the Lense Thirring effect. My question is not whether the frame dragging effect exists but rather it's manifestation in affecting ...
-3
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1answer
58 views

What solution do I need to use in this question? [closed]

Question: Jojo and Albert left the same point and hike in different directions. their displacements are $\Delta x= 4$ km and $\Delta y= 6$ km. How far are they from each other?
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1answer
36 views

How corner atom of a cube is shared by 8 atoms? [closed]

Since each atom is at the corner of a cube and 8 cubes meet at each corner. Therefore each atom is shared by 8 cubes. But I don't visualize it, so please tell how I Visualize it.
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1answer
26 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 ...
0
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1answer
27 views

$y$-component of center of a cube that rolls without slipping [closed]

For the figure above, let $O$ be the origin point for $x,y$-axis, and $+x$ goes to the horizontal right direction while $+y$ direction goes to the up direction. The figure has one circle and one ...
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0answers
30 views

Increasing the volume of a object in a photograph

I have two images which look like this --- These images are two views of a calibration object --- the white die that you see hanging in the middle. The problem is that, the die is too small and ...
3
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2answers
64 views

Kepler's First Law of Planetary Motion: Whats at the other focus? [duplicate]

Kepler's first law states that the orbit of every planet is an ellipse with the Sun at one of the two foci. Is there anything significant about the location, or any unusual properties about the other ...
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1answer
63 views

Can one calculate the distance from Earth to the camera, given a single picture?

Given an image of (part of) a sphere of known size, can one calculate the distance to the camera based on the relative size of the sphere in the image? My instinct is "no" unless you have some fixed ...
5
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0answers
31 views

Motivating Irreducibility of Hilbert Space for Quantization Axioms

In the context of geometric quantization, we usually look for a map from the Poisson algebra of classical observables to the algebra of quantum observables (or rather, a sub-algebra of the classical ...
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3answers
74 views

Finding the Direction when resolving a Vector

When you are finding the resultant of a vector I understand that to find the magnitude you use Pythagorean Theorem and I understand that to find the direction you are going to use $\tan^{-1}$ (or ...
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3answers
39 views

Deriving relationship between distance and angle for field of a line charge

The relationship $r\,\mathrm{d}\alpha = \mathrm{d}x \cos(\alpha)$ is not obvious to me. In fact, when I look at it, I think it should be $r\,\mathrm{d}\alpha \cos(\alpha) = \mathrm{d}x$. Can someone ...
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1answer
30 views

Centre of mass as a function of distance [closed]

I have searched it on Google and also visited the HyperPhysics website to find out but all they seem to offer world centre of mass of continuous and uniformly bodies.My school textbooks are of no help ...
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5answers
44 views

Particles passing through a surface

Today is the day I ask silly questions : The book says the particles passing through the surface $dS$ are the ones contained in the cylinder of volume $dS.v.dt.cos(\theta)$ but I really don't see ...
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2answers
54 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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2answers
103 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
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2answers
106 views

Number of revolutions of a rolling coin [closed]

Take two quarters and lay them on a table. Press down on one quarter so it cannot move. Then, starting at the 12:00 position, roll the other quarter along the edge of the stationary quarter. How many ...
9
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1answer
223 views

Cutting a circle and moving endpoints

A metal (or otherwise, suitably elastic) circle is cut and the points are slid up and down a vertical axis as shown: How would one describe the resultant curves mathematically?
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1answer
36 views

Error in measuring distance ignoring curvature of Earth [closed]

Suppose you model distance as a flat 2d plane rather than a curved surface. Given that the radius of the Earth is about 6400 km, approximately how far must you travel before the relative error ...
0
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2answers
66 views

How does the human eye knows how far the object from which the photon was reflected?

A photon is emitted from a source and reflected off an object (or objects) until it hits the human eye. The color of the object we see depends on the photon wavelength. If photon travels with constant ...
1
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0answers
36 views

Moment of Inertia of Polygons in the Plane [closed]

I was reading this link, which describes a method of finding the moment of inertia of a general convex polygon by splitting it into triangles. I then realized I have no idea on how to derive a such a ...
6
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2answers
94 views

Why does the $L_2$ norm give the shortest path between 2 points?

Why not the $L_1$ or $L_3$ distances? Is there some deep reason why the universe (at least at human scales) looks pretty much Euclidean? Could we imagine a different universe where a different ...
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1answer
34 views

How do I find the moment of inertia of a regular $n$-gon? [closed]

Of a regular $n$-gon with radius $R$ and mass $M$. Any hint to solving would also be acceptable. The result I'm looking for is $$I_{CM} = (1/2) MR^2 (1 - (2/3) \sin^2(\pi/n)).$$
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1answer
137 views

$c/a$ ratio for an ideal hexagonal close-packed (HCP) structure [closed]

Show that the $c/a$ ratio for an ideal hexagonal close-packed (HCP) structure is $\left(\frac{8}{3}\right)^\frac{1}{2} = 1.633$. I believe $a$ is the length of $a_1$ and $a_2$. I figured that ...
1
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1answer
60 views

Path of wheels of a bicycle

Why are the wheels of a bicycle moving in concentric circles with the center O? I know that the velocity of the back wheel is parallel to the frame of the bicycle and the velocity of the front wheel ...
1
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0answers
45 views

Bending of a pipe filled with sand

There is this industrial pipe made out of steel that is 1 meter in diameter and 6 meters long (and volume 4,71 cubic meters). The thickness of the pipe "wall" is 4 centimeter. The pipe is filled ...
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0answers
13 views

What are some structures which minimize surface stress upon expansion

Intro I am currently researching into a problem involving the cyclical expansion and contraction of a 3 layered structure comprised of an internal metal encased by another metal encased in an outer ...
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0answers
63 views

Close-packing of equal spheres - one sphere in a pyramid with a square base and four equilateral trianglular faces

I'm trying to determine the "packing efficiency" of fitting on sphere into a square based pyramidal container with four equilateral triangular faces. In other words, how much space within the pyramid ...
2
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0answers
38 views

T duality for lower codimension branes or ALF spaces

These are purely mathematical questions in some sense but I believe this is relevant in string theory as the title says. I wonder if it is possible to perform T-duality of Taub-NUT space not along ...
2
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2answers
54 views

Why should an area vector point normal to the surface?

Why is it that the direction of an area vector should be always along the normal drawn to the surface? Can't it also be some other angles with the plane?
0
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2answers
30 views

How can I calculate the center of an object relative to a focal point and a moving observer? [closed]

I'm developing an app that contains a 3D scene which the user can navigate. As the user moves it gives the illusion that you are browsing a real landscape but for the illusion to work I need to know ...
2
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0answers
59 views

Geometry topics in physics [closed]

I'd like to learn modern physics at an advanced level, but since I've no access to university, I'm self-teaching, and appeal to the Internet for information about what to study and how. Currently, ...
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0answers
40 views

Could a fourth dimension be “spatially simulated” one point at a time by using movements?

I wonder if time and movement can be translated into a simulation of an extra spatial dimension. At least in one point at a time. I'll try to explain. Imagine a fixed probe which measures the ...
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3answers
161 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
149 views

Can Minkowski spacetime be redefined as a non-flat riemannian manifold?

Minkowski space time is defined in terms of a flat pseudo-Riemannian manifold. I have wondered if it can be redefined as Riamannian manifold and in the case what type of curvature would there appear. ...
2
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1answer
126 views

Why is the inertia ellipsoid of a higher symmetry than the rigid body?

I was always puzzled by this fact. A uniform cube has a sphere-shaped inertia ellipsoid. The sphere has a higher symmetry then the cube. Is there any deep reason or implication behind it?
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2answers
139 views

A simple way of calculating Euler Angles from Rotation Matrix — help!

This is a follow up of this question : I have the rotation matrix $$ \left( \begin{matrix} a_{11} & a_{12} & a_{13}\\ a_{21} & a_{22} & a_{23}\\ a_{31} & a_{32} & ...
1
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1answer
201 views

Inertia tensor of a spherical cap

I'm trying to calculate the inertia tensor of a spherical cap (a piece of a sphere) like the one shown below. The origin (not shown) is located at the center of the whole sphere and the axes ...
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2answers
95 views

Euler angles derivation

I have been trying to grasp the idea of Euler angles for a while. Can anyone point out if my understanding is correct or not. Situation: We have 3 axes known as principal axes of inertia which define ...
0
votes
1answer
141 views

Leg Press & Actual Lifted Weight [duplicate]

I was doing leg press at the gym today and was curious how much weight I actually lift when I do the exercise as compared to when I do a squat. Suppose I load $w_L$ onto the machine, which has an ...
2
votes
1answer
31 views

random particles on a grid: Effect of increasing density on distance between them

Say I have two boxes which both contain, say, 25 red particles (as shown in picture). These particles are randomly placed in a 2d grid, and in one the total area $A_{1}=20000$ and the other has area ...
7
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1answer
1k views

How to calculate roll, yaw and pitch angles from 3D co-ordinates (Euler Angles)

I have digitized a video of a flying fly in a 3-dimensional space. At all instants I know the x, y, and z co-oridinates of the following points on the fly's body --- The points are my choice, and ...
2
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1answer
87 views

Measuring the nearest order of magnitude

The world's largest ball of a string is about $R=2 m$ in radius. To find the nearest order of magnitude, what is the total length $L$ of the string in the ball? I have tried this in the following ...
2
votes
1answer
102 views

Relative strength of a dome [on hold]

Is there a rough way to determine how the height of a dome affects the load that dome could support? For instance, assuming the bases of two domes are 24" in diameter, and one dome is 2" high while ...
2
votes
4answers
669 views

Electric Field due to a disk of charge. (Problem in derivation)

This might be a really silly question, but I don't understand it. In finding the electric field due to a thin disk of charge, we use the known result of the field due to a ring of charge and then ...
5
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1answer
221 views

Why is $S^1\times\mathbb{R}^{n-1}$ the topology of $AdS_n$?

Anti-de Sitter $AdS_n$ may be defined by the quadric $$-(x^0)^2-(x^1)^2+\vec{x}^2=-\alpha^2\tag{1}$$ embedded in ${\mathbb{R}^{2,n-1}}$, where I write ${\vec{x}^2}$ as the squared norm ${|\vec{x}|^2}$ ...