Questions tagged [geometry]

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

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When a bus goes around a corner, does the person sitting at the back travel further distance than the person sitting at the front?

This is a bit of childish question. When a bus goes around a corner, does the person sitting at the back travel further distance than the person sitting at the front? My thought is no because the bus ...
SteamMarine's user avatar
0 votes
0 answers
13 views

How to approach a static analysis when objects are on differing inclines?

I think this sort of problem is known and relatively simple when on a single angle of incline, but I'm trying to understand a problem with two points of contact of a uniform vehicle where each contact ...
kilxi's user avatar
  • 1
-2 votes
1 answer
35 views

Why cant we draw 7 points perspective drawing or more? [closed]

This is a simple question. I think it is impossible to draw 7 or more points of perspectives in a piece of paper, but is it possible? if not, why? Even DALLE cant draw it even 6 points.
Nephalen Arara's user avatar
0 votes
0 answers
27 views

Proof for law of reflection with geometry only [closed]

I aim to prove, using pure geometry, that the path of light from point A to B, reflecting off a plane mirror, is minimized when the angle of incidence equals reflection. I am trying to use the method ...
user395979's user avatar
0 votes
3 answers
52 views

Is the radius equal to length/radians? [closed]

Is the radius equal to the length/radians. Since the circumference is 2 pi times r and radians of an entire circle is 2 pi r should be equal to lentgh/radians I needed this proof to understand why we ...
Thedambamjam's user avatar
0 votes
4 answers
108 views

How can a triangle have a sum exceeding 180 degrees in a curved space?

I was reading a book to understand the limits of the euclidean space I understand that lines that are parallel in 2d can meet in 3d space like on a sphere but it is hard to imagine or fathom why the ...
lodo's user avatar
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0 answers
54 views

Determine the equation of earth's orbit

I am trying to find the the equation earth's orbit using Kepler's Scheme. After every 1.88 years Mars returns to its initial position in the sky. With reference to the diagram and data below find the ...
sameed hussain's user avatar
-2 votes
2 answers
84 views

In real life, we can have a pencil of length 2 cm. Can we have pencil of length $\sqrt{2}$ cm? [duplicate]

In real life, we can have a pencil of length 2 cm. Can we have pencil of length $\sqrt{2}$ cm? My answer to that was no , we cannot even make 2 cm pencil. My argument was that when are working ...
user avatar
0 votes
0 answers
43 views

Why is time taken to go around the Sun to cover a small fixed angle proportional to the square of the distance?

I am reading Feynman's lost lecture. At this point, he asks us to consider points J, K, L and M which subtend equal angles at the sun S. And then he claims that triangles JKS and KLS are similar ...
Neeladri Reddy's user avatar
3 votes
2 answers
448 views

Geometry of anticommutation relations

I am asking this question as a mathematician trying to understand quantum theory, so please forgive my naivety. Systems satisfying the canonical commutation relations are naturally modeled with ...
Cole Comfort's user avatar
0 votes
0 answers
27 views

Carbon Nanotube Modeling

In various references, we see the construction of unit cells of carbon nanotubes from chiral and translational vectors. The chiral vector is given as: $$\vec C_h = n\vec a_1 + m\vec a_2$$ While the ...
benjamin_ee's user avatar
0 votes
1 answer
29 views

Does anyone know of published data on Mach interactions with various asymmetrical toroids?

I was looking for any lab conducted tests, or computer models of Mach reflections off of different toroids. How would shock waves propagate through asymmetrical 180° ring toroids, what kind of ...
-1 votes
1 answer
72 views

How fast do I have to fly vertically up to pause sunset?

I'm standing on the famous Laguna Beach in southern Los Angeles to watch the sunset on December 18th (33.541679°N 117.777214°W, 0m elevation, 16:44 PST). Now, from my perspective at the shore, the sun'...
Richard Zhu's user avatar
2 votes
0 answers
51 views

How much of an observer's field of view will be black upon crossing an event horizon? [closed]

The aberration of light will cause an observer to still see a black hole as "distant" when the event horizon is crossed. This means that if the observer looks directly toward the center of ...
Patrick O'Brien's user avatar
1 vote
1 answer
68 views

About Plane motion [closed]

An excerpt from a book I read: “In reality, objects are moving in a 3-dimensional space. However, if the acceleration of the object is constant, then there must be a certain plane which contains the ...
Samuel Tse's user avatar
24 votes
1 answer
7k views

Based on my calculations, we cannot see the Earth from the ISS. Obviously it's wrong. Why?

What started as a fun exercise really annoys me because I cannot see where I got it wrong. I initially wanted to see how many photons hit a pixel of a camera on the ISS pointed at the Earth - but I ...
Mister Mystère's user avatar
2 votes
4 answers
484 views

Is buoyancy affected by container geometry? [duplicate]

Is it possible for something that can't float in a rectangular container to float in a triangular container?
Mason Valentine's user avatar
1 vote
0 answers
78 views

Similar to how there's field lines that make equations in Newtonian Gravity more intuitive, is there something that makes GR equations more intuitive?

One way I know to get intuition for the derivation of the force equation $$F=\frac{GM_1M_2}{r^2}$$ in Newtonian Mechanics is to imagine gravitational field lines, in combination with certain ...
Anders Gustafson's user avatar
0 votes
0 answers
61 views

What is heard when a tuning fork is struck?

When a tuning fork is struck I hear two tones. From a distance I can hear a high octave frequency of the pitch of the tuning fork. Though, if I listen to it closely (closer to my ears), I also hear a ...
Lecifer's user avatar
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1 vote
1 answer
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Is it possible for 4 satellites cannot render a position fix on Earth?

I recently learnt about how GPS works and how it uses the intersection of spheres to locate a person which got me thinking whether 4 spheres can always guarantee a position fix. My understanding is ...
Nullity's user avatar
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2 votes
1 answer
143 views

Is the celestial sphere we actually see the Riemann Sphere?

I've been watching a few lectures by R. Penrose where he seems to say that what we see around us is the Riemann sphere. He usually gives the example of an observer floating in deep space or if the ...
Svenn's user avatar
  • 31
1 vote
2 answers
101 views

The difference in path lengths for waves in the double slit experiment

Fig.1 I don't quite understand the diagram, because it shows $L_1$ and $L_2$ as parallel, even though they are supposed to meet at the same point. I believe the idea is that $\Delta L$ approaches $d \...
user110391's user avatar
-1 votes
2 answers
254 views

$r_1+r_2= A$ in prisms

In class we derived a result which said that the sum of the 2 angles of refraction in a triangular prism $r_1+r_2$ is equal to the angle of the prism $A$. The proof goes like this Over here, it is ...
Pumpkin_Star's user avatar
1 vote
1 answer
52 views

Tetrahedral Geometry and Potential energy

Intuitively, I'd think it possible to use potential energy to find the bonding angles in methane, but I'm not getting the right answer. Am I missing something? In a tetrahedral, the faces are ...
R. Romero's user avatar
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0 votes
1 answer
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The Plus/Minus sign on Forces in a Cartesian coordinate system

I have been struggling with Forces in a Cartesian Coordinate System and whether to understand what signs to put on to solve simple problems in the view of mathematics. Let's make a simple one ...
Draginev's user avatar
0 votes
3 answers
125 views

Representing special relativity on the hyperbolic plane

I recently gave a presentation on hyperbolic geometry and included mention that space-time is hyperbolic, but was not able to adequately explain what this means. To demonstrate how space-time is ...
Zaz's user avatar
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0 votes
1 answer
54 views

Relative velocity in SR as tangent of both Euclidean and hyperbolic angle?

When drawing a Minkowski diagram, one chooses a frame of reference whose axes are painted perpendicular to each other. Given a second frame that is moving in the positive X axis of the first at ...
Sierra's user avatar
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5 votes
0 answers
280 views

Every possible QFT from positive geometry?

Physicist Nima Arkani-Hamed has taken an interesting approach to understand fundamental physics based on geometry (specifically, positive geometry constructions). This started with his work with ...
vengaq's user avatar
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2 votes
0 answers
55 views

If the radius of a sphere is reduced by half due to relativistic length contraction, will the volume also be half?

We know that volume is cubicly proportional to radius of a sphere. But if the radius is become half due to relativistic Length contraction, it's being reduced from only one dimension, not three. And ...
Zeesan's user avatar
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1 vote
1 answer
124 views

Examples of vectors which are Non-euclidean [closed]

I am watching Tensor for beginners by Eigenchris, and I was confused when he said that, not all vectors are Euclidean. So, can someone explain me the meaning behind this by an example or visualisation ...
My Essential Learning's user avatar
0 votes
1 answer
29 views

Proof for Number of Images by Inclined Mirrors

I learned that the formula for the number of images formed by a pair of plane mirrors is given by $$N = \frac{360^{\circ}}{\theta} - 1$$ But, when $\frac{360^{\circ}}{\theta}$ is odd and the object is ...
Srish Dutta's user avatar
1 vote
1 answer
119 views

Vectors forming a closed triangle

I've always been taught that vectors that form a closed polygon represent an object being at equilibirium, that is there is no resultant force on the object. However, this has never been intuitive to ...
Jeremy Clarkson's user avatar
1 vote
0 answers
99 views

Geometric tricks in general relativity?

So I was quite surprised when I had learned some geometric tricks in school but didn't see them applied in the geometry of general relativity. Here's what I'm talking about, let's say I have $2$ ...
More Anonymous's user avatar
1 vote
1 answer
128 views

When do we use dot product and when do we use cross product? [closed]

I actually dont understand that when do we use cross product and when to use dot product ……it is very difficult to remember that a torque is cross product and work done is dot product. please tell me ...
Physics student's user avatar
2 votes
1 answer
84 views

Measuring Earth's circumference in Genius documentary by Hawking

I was watching the first episode of the Genius documentary series by Dr. Hawking. At the beginning of the documentary, the people prove that the Earth is round and not flat by going to a lake, and ...
Taela Shanthi's user avatar
0 votes
0 answers
38 views

Does a tangential vector experience length contraction when moved in radial direction through Schwarzschild metric?

Let's have a look at the Schwarzschild solution. Let's consider only the spatial part since my question is only regarding length contraction. There is the coefficient of the radial component, it's $\...
Scibo's user avatar
  • 93
22 votes
7 answers
5k views

Is there a *geometric* explanation for why photons have no rest frame?

I've read the various threads on this site that talk about it being impossible for photons (or massless particles in general, really) to have a rest frame, and the answers all seem to boil down to &...
Mikayla Eckel Cifrese's user avatar
2 votes
1 answer
59 views

Apparent size of and object [closed]

How can i prove that the apparent size of an object Is inversely proportional to the distance from the observer?
Antonio Puca's user avatar
2 votes
2 answers
410 views

What is the cardinality of intervals in space, and what is the cardinality of intervals in spacetime?

The interval $|(0, 1)| = |\mathbb{R}|$. I naively thought that one could treat intervals in space in kind, i.e., that the cardinality of any interval in space has the cardinality of the continuum. You'...
Andres's user avatar
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0 votes
1 answer
91 views

How do we represent a vector (or a point) in spherical coordinates (if its given in cartesian coordinates)?

Its easy to locate points and vectors cartesian coordinates using the good old, 3i+4j+5k which says go 3m in direction of i, and j and k. This might represent the direction some force acting on ...
Rohit Shekhawat's user avatar
3 votes
3 answers
120 views

Can 2 vectors in dimensions greater than 3 be found on a plane? [closed]

I was thinking about how, given any 2 linearly independent vectors in a 3D cartesian coordinate system, one can always find another 3D cartesian coordinate system (or should I say frame) where the 2 ...
bluesky's user avatar
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0 votes
0 answers
44 views

Can some of the (timelike) curves which make up a (timelike) congruence be tangent to each other? (Or are they all strictly disjoint?)

A congruence is a useful notion in general relativity, relating mathematcal definition and physical interpretation: "A congruence (more properly, a congruence of curves) is the set of integral ...
user12262's user avatar
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1 vote
0 answers
73 views

Transforming a Cauchy foliation of $(1+1)$ Minkowski plane and building out the product manifold: Is the result a valid spacetime or component of one?

Consider a spacetime $(\zeta^{3,1},g)$ where $$g=\frac{dudv}{uv}-\frac{dr^2}{r^2}-\frac{dw^2}{w^2} \quad \forall u,v,w,r \in (0,1)$$ Now this is just Minkowski space in different coordinates (related ...
geocalc33's user avatar
2 votes
4 answers
256 views

Show that $d\mathbf{v}^2/dt = 2\mathbf{v}\cdot d\mathbf{v}/dt$ using geometry only

I have just begun reading Modern Classical Physics by Thorne and Blandford and I am trying to wrap my head around their "geometric viewpoint" on classical mechanics. The first exercise in ...
Nic Christopher's user avatar
0 votes
2 answers
206 views

Proof of the second Bianchi identity

Suppose $\omega$ is a connection one-form, and the curvature tensor is defined as $$R^a_{~~b} = d\omega^a_{~~b} + \omega^a_{~~c}\wedge \omega^c_{~~b}~,$$ where the latin indices refer to the fact that ...
newtothis's user avatar
  • 611
1 vote
1 answer
48 views

A noon cannon with two lenses

A noon cannon usually has a single convex lens which focuses sunlight onto a fuse. The cannon contains gunpowder. The fuse ignites and the gun discharges at noon. https://en.wikipedia.org/wiki/...
SamJ's user avatar
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1 vote
0 answers
43 views

Satellite angular velocity at an angle

Suppose I am observing a satellite that is not at my zenith. I know the altitude(α) and azimuth(γ) of my telescope and I was able to get a relative angular velocity of the satellite. Based on this ...
ryanx's user avatar
  • 11
0 votes
0 answers
33 views

Resolving Vectors [duplicate]

When resolving vectors into their horizontal and vertical components, why must the individual vectors form a closed triangle? I don't understand why vectors must form a closed triangle when one vector ...
Jeremy Clarkson's user avatar
0 votes
1 answer
93 views

An application of spherical trigonometry to the celestial sphere

In the book 'An Introduction to Modern Astrophysics' (Carroll and Ostlie, 2017), the first chapter presents an application of spherical trigonometry. At a certain point, the authors derive an equation ...
Sarah's user avatar
  • 3
0 votes
2 answers
119 views

Basis of body centered cubic latice

For the past few days I've been studying solid state physics and more specifically I have been busy with the crystal structures. I was just making some exercices and on of them asked me to give the ...
luki luk's user avatar
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