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

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Standardising shadow length on sundials

The sundial is fundamentally flawed in that the length of each hourly shadow changes with the seasons. If the base of the sundial was engineered to move cyclically on an anual basis however, the ...
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2answers
47 views

What should the length of my wire be in order to get a surface area of 10cm^2?

I would like to make a flat coil out of a steel wire that is $1.22 ~\text{mm}$ in thickness (or $1.22~\text{mm}$ in diameter). I wish to make the coil up the wire into a flat disk that has a surface ...
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3answers
24 views

Foci of elliptical path

I have read the Kepler's laws of motion where I came across the term foci of elliptical path. But what is really a focus? Can anyone please explain what is a focus (maybe with a diagram) and why a ...
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1answer
40 views

Why do you seem to go faster as you hug a turn?

I was driving to work this morning when this question occurred to me. I was going up a clover-leaf entrance ramp to the highway. The person in front of me was lazily floating the outside of the curve, ...
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0answers
16 views

Circumference measurement using a capacitive sensor

I have a question which I hope someone in here can help me answer. Background: I’m building a device where I intend to use a stretchable capacitive sensor to define the radius change of an object. ...
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2answers
34 views

How to calculate centre of mass

How do I find the centre of mass with given coordinates? For example if we have four objects with mass $m$ at coordinates of a square $(0,0,0),(0,0,a),(0,a,0),(0,a,a)$ or another example with eight ...
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0answers
19 views

Constructing uniform mesh in reciprocal space?

This is a bit of a mental exercise for me to get comfortable with the math of reciprocal spaces since I am going to start doing some research that requires knowledge of reciprocal spaces. Let's say I ...
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1answer
49 views

How to derive path difference ($\Delta l=d\sin \theta$) for double-slit interference?

The Wikipedia page for the double-slit wave interference experiment states that the path difference between waves diffracting from the two slits is equal to: $$ \Delta l=d\sin \theta $$ where $d$ is ...
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3answers
217 views

Are circles stronger than triangles?

I've often herd in engineering that "there is no shape stronger than a triangle". I also recall that arches are very strong shapes as well, which can be crudely described as a ...
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0answers
158 views

Can the universe be round but still infinite?

Can the universe still be infinite in space if its curvature is > 1? Is a manifold of positive curvature necessarily compact? Does the Tarski paradox have any bearing on the finite or infinite ...
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1answer
276 views

Why are three parameters required to express rotation in 3 dimension?

We know that in spherical coordinates angle $\theta$ and $\phi$ (two angles)are enough to express three dimensional rotation of matrix. But to express rotation mathematically as a transformation ...
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25 views

Radian Zeno-version paradox: Can a particle moving in the circular path reach the angular position of non-terminating decimal form radian value?

Consider a particle P moving in a circle of radius r as shown in the figure. Premise 1: Position of the particle can be described by the angle $\theta$. Premise 2: Particle reaches the position ...
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1answer
74 views

Constrained Motion of Connected Particles, Small Calculation Question

I am looking at this sample problem from Meriam Kraige - Engineering Mechanics Dynamics: When I do the differentiation, I end up with $\large -2\dot y+\frac{x}{\sqrt{x^2+h^2}}$ Where is the $\dot ...
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1answer
206 views

Center of mass of equilateral triangle

I'm trying find the center of mass ($R$) of a uniform density equilateral triangle without using symmetries to find the x coordinate of the vector $R$, but I can't get the expected $R_x = ...
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1answer
57 views

Calculating the area of region of the sky

I am given the right ascensions ($\alpha_1$ and $\alpha_2$) and declinations ($\delta_1$ and $\delta_2$) of a specific region of the sky. How can we find the area of this region? I know that there ...
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3answers
1k views

How many times can light revolve around a black hole?

Take a light ray approaching a black hole from infinity which goes out again to infinity. What is the maximum finite rotation it can describe? (I know it can loop around indefinitely in the ...
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0answers
51 views

Justifying the use of real numbers for measuring length

I am not sure if this is the most appropriate place to post this but here goes nothing: Assume we were trying to come up with system of numbers $S$ to model our intuition of length. We want $S$ to ...
18
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4answers
2k views

Distinguishing between solid spheres and hollow spheres (equal mass)

If there are two spheres (hollow and solid) with equal mass and radius and we want to find the hollow sphere without using any equipment. What's the best way(s) to recognize the hollow sphere and ...
0
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1answer
44 views

Quantum physics and constructable numbers [duplicate]

I do not know much about quantum physics. However, I do know it believes the world is discrete ( has quanta). This seems to contradicts the fact that we can create an object of length root 2 since you ...
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0answers
23 views

Is the total length of the inner sheet of a two ply roll of toilet paper shorter than the outer sheet?

If you look at any individual square of two plies, each ply looks the same. But musn't the inner ply be shorter? Wouldn't the inner ply develop kinks if it was the same length as the outer ply? Or ...
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1answer
32 views

Electric Flux - Vector Components

How is $vcos(\theta)$ the perpendicular vector? I think I'm missing something fundamental in my trig and vector knowledge...
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0answers
31 views

Why is space 3 dimensional and could it be different? [duplicate]

Is there any particular physical law or property which caused space to be 3 dimensional, and is there theoretical possibility of having more or less dimensions in physical space?
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2answers
143 views

What is the connection between geometry of physical space and Hilbert space?

In Quantum Mechanis (QM), the dynamical variables are the (quantized) coordinates $x_j$ and their canonical conjugate $p_j = -i\partial_j$ with the commutation relation $[x_j,p_k]=i\delta_{jk}$ ...
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43 views

What's wrong with this calculation of the center of mass of a triangle?

Find the center of mass $(x_G,y_G)$ of a homogeneous triangle of mass $m$. Divide it into infinitesimal rectangles of width $dy$, length $x$, mass $dm$ and area $dA$. We have $d A = x dy $ ...
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1answer
71 views

Weight of an object at different angles [closed]

I'm trying to either find a calculator online or help with an equation to work out how much weight I'm lifting when I pick up my dirt bike off the floor [edit: when it's lying on it's side on the ...
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2answers
96 views

Poisson equation in 2D and 3D: geometrical reason for the difference

The Poisson equation in 3D shows a fundamental solution in 3D which decays with $\sim 1/r$, whilst in 2D it shows a much different decay $\sim -\ln r$. While in 3D not only the solution, but also its ...
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0answers
40 views

Is there a theory that physically explains the origin equivalence principle / explains gravity via acceleration?

I've been thinking about how gravity could arise from a 4th dimensional spinning cylinder with space-time that has pliability like rubber (which I think is a generally accepted analogy). The ...
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1answer
108 views

How do you calculate the focal point location of a circular mirror? [closed]

I'm trying to find the focal point and center of curvature of a concave mirror. Just using the radius for the center doesn't seem to work. I know C = 2f, but I'm not sure how to find f or C, given the ...
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1answer
107 views

Snell's law demonstration

I'm a bit confused about a Snell's law demonstration. I'm reading Communication Systems from W. Tomasi. In the chapter 11, the author applies the Snell's law to θent, and -here comes my problem- he ...
2
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1answer
94 views

Geometry, Group Theory, and Statistical Mechanics

During the course of my first statistical mechanics course we generally concerned ourselves with a bulk amount of our system and considered it in terms of a set of lattice sites that had a state. How ...
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2answers
523 views

Spacetime geometry around two black holes

For space-time geometry we all know images like he one below. But if I were to take a neutron star and put it right next to but not touching a black hole what effect would that have on the geometry of ...
6
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1answer
116 views

Null Coordinates

I have a very basic question: what are the advantages of writing a metric in the null coordinates? Which extra insight do they provide? I've looked in Caroll's "Spacetime and Geometry" and Wald's ...
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2answers
201 views

How were the ratios of distances between planets and the Sun first calculated?

I was reading some literature and I found that long before the actual distances between other planets and Earth or distance between Sun and Earth were known, physicists had calculated the ratios ...
106
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2answers
6k views

Why do sunbeams diverge even though the sun is much more than a few kilometers away?

Consider this picture of sun beams streaming onto the valley through the clouds. Given that the valley is only (at a guess) 3km wide, with simple trigonometry and the angles of the beams, this ...
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2answers
102 views

4- dimensional space geometry, what is the point? [closed]

I just read about the 4 dimensional space. I found a nice article describing how to visualize a 4-D object into our 3-D world. This is really fascinating. However, what's the point of researching in ...
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1answer
57 views

How do I calculate the right ascension of the points along the ecliptic at given elevations?

How do I calculate the right ascension of the point along the ecliptic nearest the sun at sunset and sunrise that is at a given altitude/elevation? For example, I'd like to compute the right ...
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4answers
273 views

Why drops form spheres?

Consider a drop of water floating in an inertial frame in STP air (e.g., the ISS). Intuitively, the equilibrium shape of the drop is a sphere. How would one prove that? Is it equivalent to showing ...
5
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1answer
91 views

Gravity on and inside a planet-sized bi-lobed body

Admittedly, for yet another science-fiction project Say I have a planet-like body shaped like a sphere with a torus subtracted out of it, leaving a sort of "apple core" shape. Firstly, is the ...
0
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1answer
129 views

How to calculate the horizon line of a satellite?

I need an equation to calculate a list of Earth-centered, Earth-fixed (ECEF) XYZ coordinates on the earth that represent the visibility limit of satellite given its ECEF XYZ coordinates. For any ...
2
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2answers
1k views

Is it possible to calculate the length of a tube if the 'near' diameter and 'far' diameter are known?

When looking down and through a length of tube, the 'far' diameter is less than than that diameter that is closest to the viewer's eye. If, for example, the tube's internal diameter is measured at ...
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0answers
43 views

Maps on manifolds

I am reading the SUPERGRAVITY textbook of Freedman and Van Proyen. I am reading that in the sphere we can introduce two patches that their union covers the whole sphere. Ok, I understand why we need ...
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0answers
67 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
77 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 ...
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2answers
66 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 ...
0
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1answer
52 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 ...
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1answer
71 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
69 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
56 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 ...
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1answer
32 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
36 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 ...