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

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0answers
79 views

Geometry and physics [closed]

I'm searching for references, articles and books, that discussed the geometrization of modern (and contemporary) physics, in a philosofical point of view. Something in the way that Michael Friedman ...
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1answer
84 views

3D billiard with no gravity nor air drag

If I have a projectile shot in a vacuum-box that has no gravity or wind resistance inside it (lets say the box is 1000 units tall and 1000 units wide), with the only rule being that the projectile ...
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2answers
4k views

Finding the drag force (Air resistance force) for accelerated ball?

As you know if I want to find the force for an accelerated object I will use the law $F_o=ma$ so I can get the affecting force of it. But there is another force affecting against the object. It's the ...
6
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2answers
547 views

Are there any naturally occurring perfect circles? [duplicate]

Given that $\pi$ is the irrational number that occurs with a perfect circle, and perfection is very difficult to achieve through chance or nature, I think that most circles are really ovals, and ...
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1answer
1k views

Minimum height of mirror required to view image

I wanted to know the minimum height of mirror required to be able to view a complete image of a person. I considered the following setup: $HF$ is the person in question. $H$ denotes the head, $F$ ...
1
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2answers
271 views

At what starting angle will a billiard ball hit a pocket? [closed]

Let's say you have a square pool table with one pocket. At what angles can you hit the ball to make it hit the pocket? What relation do these angles hare? Constraints: Table is square: $\ell=b$. ...
2
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2answers
159 views

Determine the effective radius of a gear?

I'm trying to determine the gear radius using a ruler by $cm$ but I just don't know what to measure: 1- the length from gear center point to the end of the gear tooth ? Or 2- the length from gear ...
2
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2answers
215 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 ...
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2answers
80 views

What is a geometrical object?

From the Wikipedia link for Geometry: Geometry (Ancient Greek: γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position ...
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2answers
184 views

Triple-right triangle experiment: what's the minimum distance?

Among the other ways, one way to prove the Earth is round is the triple-right triangle. The idea is simple: Starting from point A you move in a straight line for a certain distance. At point B, ...
5
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2answers
266 views

Is length/distance a vector?

I have heard that area is a vector quantity in 3 dimensions, e.g. this Phys.SE post, what about the length/distance? Since area is the product of two lengths, does this mean that length is also a ...
5
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2answers
96 views

Which causal structures are absent from any “nice” patch of Minkowski space?

Which "causal separation structures" (or "interval structures") can not be found among the events in "any nice patch ($P$) of Minkowski space"?, where "causal separation structure" ($s$) should be ...
2
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1answer
102 views

Perfectly focusing refractive surface

On reading Feynman's lecture on physics, in the geometrical optics section he said that a curve which focuses all the rays coming from a point to another fixed point beyond the refracting surface ...
0
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1answer
36 views

Is there a term for the argument of the sine function outside of geometry?

Are there similar terms in other areas for the idea the "angle" conveys in geometry? I find that functions for abstract things such as pressure, electrical currents (nothing geometric there) on AC ...
8
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4answers
285 views

Physical representation of volume to surface area

I was looking at this XKCD what-if question (the gas mileage part), and started to wonder about the concept of unit cancellation. If we have a shape and try to figure out the ratio between the volume ...
0
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2answers
126 views

Limit on velocity in Minkowski Spacetime geometry

Let A be a rocket moving with velocity v. Then the slope of its worldline in a spacetime diagram is given by c/v. Since it is a slope, c/v = tan(theta) for some theta > 45 and theta < 90. Does ...
3
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1answer
99 views

Uniqueness and existence of polygonal orbits through a spherical shell

Say we have a spherical wire mesh raised to a negative voltage. Then let's say we release a proton from near the surface, and away from the surface, at some angle and speed. Also, imagine that the ...
0
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2answers
104 views

Where to take $\theta$ (theta) in a triangle?

This is an inclined surface having and unit vector A. The perpendicular and horizontal surfaces are the components of the inclined surface. We want to find out that how much flux will pass through ...
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1answer
103 views

Rømer's determination of the speed of light

I am trying to understand Rømer's determination of the speed of light ($c$). The geometry of the situation is shown in the image below. The determination involves measuring apparent fluctuations in ...
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2answers
603 views

How to determine Center of Gravity? [closed]

I came across this question while having conversation with one person. We know that Center of Gravity of a solid cube is at the intersection of connecting the opposite vertex of the cube. Suppose, you ...
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0answers
66 views

Geometry for Physics [duplicate]

I am currently a high school student interested in a research career in physics. I have self taught myself single variable calculus and elementary physics upto the level of IPHO . And I am comfortable ...
0
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0answers
27 views

Problem in geometrical optics [duplicate]

I was trying to solve a problem taken from an Physics Olympiad when I came across a curious and complex mathematical expression. I can not prove with what I know so far about mathematics, does could ...
1
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1answer
31 views

Asking about centrepetal acceleration

please look at the fig first 1) How can you claim that the triangle ABC is same as the triangle PQR? 2) How can you claim that the angle between V1 and V2 is same as the angle between AC and AB? ...
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2answers
317 views

Geometrical interpretation of complex eigenvectors in a system of differential equations

Let's consider a system of differential equations in the form $$\dot{X} = M X$$ in two dimensions ($X = (x(t), y(t))$). In the case that $M$ has real values, it is easy to give a geometric ...
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2answers
690 views

Calculate the center of mass of a semicircle [closed]

How I determine the center of mass of a semicircle using the definition of center of mass? I only know solve this using the Pappus theorem. Consider that the semicircle is centered on the origin and a ...
3
votes
2answers
153 views

Proof that a spherical lens is stigmatic

In geometric optics, we generally allow that, for example in the case of a convex lens, rays coming from a particular point get refracted towards another particular point on the opposite side of the ...
4
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1answer
339 views

How is the equation of motion on an ellipse derived?

I would like to show that a particle orbiting another will follow the trajectory \begin{equation} r = \frac{a(1-e^2)}{1 + e \cos(\theta)}. \end{equation} I would like to do this with minimal ...
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0answers
65 views

Water Stream from a Horizontal Surface

If water was projected from a flat surface where gravity was equal all over the surface. What would happen when the water fell in on itself? The water is in a continuous stream and is perfectly ...
3
votes
1answer
401 views

Nanotube chiral angle as a function of $n$ and $m$

I'm looking into nanotubes and I thought I'd assure myself that the basic geometry equations are indeed correct. No problems for the radius, I quickly found the known formula: $$R = ...
4
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1answer
122 views

How to assign coordinates to the elements of a flat metric space

Consider the metric space $(M, d \,)$ where set $M$ contains sufficiently many (at least five) distinct elements, and consider the assignment $c_f$ of coordinates to (the elements of) set $M$, $c_f ...
4
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1answer
131 views

Flat space metrics

This question concerns the metric of a flat space: $$ds^2=dr^2+cr^2\,\,d\theta^2$$ where $c$ is a constant. Why is it necessary to set $c=1$ to avoid singularities and to restrict $r\ge 0$? Thanks.
2
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1answer
127 views

Can we project a 4D world using 3D video technology?

Traditional movies, TV, etc, faithfully show our 3-dimensional world using 2 dimensions. So can we have a movie that shows a 4-dimensional world using 3D technology?
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10answers
989 views

Is it possible for a physical object to have a irrational length?

Suppose I have a caliper that is infinitely precise. Also suppose that this caliper returns not a number, but rather whether the precise length is rational or irrational. If I were to use this ...
2
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5answers
597 views

Do perfect spheres exist in nature?

Often in physics, Objects are approximated as spherical. However do any perfectly spherical objects actually exist in nature?
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2answers
394 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, ...
5
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2answers
296 views

Space-time geometry and metric

I am confused in one question in general relativity, why we can always express a space-time geometry only by metric. It means a metric, which is just about distance in tangent space, can tell us all ...
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2answers
5k views

What is the characteristic length of a cylinder

I have a cold cylinder that is submerged in hot water and I need to find the convective heat transfer coefficient. I can do the whole process but I am stuck finding the characteristic length. I found ...
2
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0answers
58 views

Dirichlet's work on gravity in non-Euclidean space?

In the book The Norton History of Astronomy and Cosmology by the late John North I have found the following statement (page 514): "The German mathematician Lejeune Dirichlet studied the law of ...
2
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1answer
687 views

Tiling hexagons on a sphere surface

In attemopt to understand basic principles of non-Euclidean geometry and its relation to physical space, I am reading General Relativity by Ben Crowell. On page 149 there is a discussion of hexagons ...
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0answers
138 views

Inscribed and Escribe Squares and Circle [closed]

Assume a circle(a) of diameter d. Inscribe a square A centred in the circle with its diagonal equal to the diameter of the circle. Now escribe a square B with the sides equal to the diameter of the ...
3
votes
5answers
160 views

Why is the world sheet of an open string a cylinder?

I went to a lecture a few weeks ago and was told the following: The world sheet of a closed string is a normal, standing cylinder. The world sheet of an open string is a cylinder on its side. This ...
4
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1answer
193 views

How would one calculate the amount of water contained in a cloud?

So I was looking out the sky one day and I wondered how I would go about calculating how much water was contained in a cloud. I figured the following simple outline 1) We need to roughly know how big ...
2
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0answers
136 views

Getting the AdS metric from maximally symmetric spaces

I am familiar with the way we derive the form of the FRW metric by just using the fact that we have a maximally symmetric space i.e the universe is homogeneous and isotropic in spatial coordinates. ...
-1
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1answer
383 views

Internal forces in a truss and its geometry

I'm to work out the internal forces in a truss, but I can't get my head around the geometry of the truss itself. I'm starting to think there may have been information on the diagram which I missed. ...
2
votes
1answer
141 views

How far does typical view of clouds/atmosphere extend?

The specific "sub questions" I'm asking are: When you are looking at clouds just on the horizon, how far away would they be? How wide (in km) is that total field of vision at roughly cloud height. ...
1
vote
1answer
206 views

The equation of a ferrofluid under a magnetic field?

What is the parametric equation guiding the geometry of a ferrofluid under a magnetic field? See also this Wikipedia page. From previous research, Maxwell's Equations and Navier-Stokes Equations were ...
3
votes
1answer
243 views

Is Dyson Sphere a stable construction?

Suppose that a star is encompassed by a Dyson Sphere. Do we need a position control system for the Dyson Sphere to keep its origin always aligned with the center of the star? Will it stay aligned ...
3
votes
2answers
274 views

Shape of electric charges on sphere in equilibrium state

When electric charges of equal magnitude and sign are released on a regular sphere (and assume that they stick to the surface of the sphere, but they are free to move along its surface), what is the ...
2
votes
2answers
5k views

Determining the center of mass of a cone

I'm having some trouble with a simple classical mechanics problem, where I need to calculate the center of mass of a cone whose base radius is $a$ and height $h$..! I know the required equation. But, ...
2
votes
1answer
218 views

Why is physical space equivalent to $\mathbb{R}^3$?

Why is physical space equivalent to $\mathbb{R}^3$, as opposed to e.g. $\mathbb{Q}^3$? I am trying to understand what would be the logical reasons behind our assumption that our physical space is ...