# Questions tagged [geometry]

To be used for questions on geometry closely pertaining to physics. Includes differential geometry and Euclidean geometry. Do prefer the more specific tag differential-geometry for questions about differential geometry.

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### Conception of earth's size based on the width of the observable horizon when standing at sea level and the circumference of the earth

As an aid to conceiving of the size of the earth, using the information that the horizontal (left to right or right to left) width of (not the distance to) the observable horizon when standing at sea ...
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1 vote
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### Discovery of a Formula for Geostationary Orbit Distance: Seeking Expert Feedback [closed]

I’m an amateur enthusiast without a formal academic background in mathematics or science. Recently, I stumbled upon an idea and derived a formula that I believe calculates the distance traveled along ...
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### Throwing a ball in the air

When we throw a ball in the air, we know that if we do not throw it too high, then g can be held constant over the trajectory and we can approximate the curve by a parabola. However we also know that ...
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### Collection efficiency of mirror

I want to compare plane and parabolic mirror for collection of photon from a point source. Intuitively, parabolic mirror focuses all rays from point source and gives parallel rays therefore has a ...
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### Does the term $d ( \omega_{ab} \wedge \theta^a \wedge \theta^b )$ have any significance?

If $\omega_{ab}$ is the spin connection 1-form, and $\theta^a$ are the tetrad 1-forms, then one has the equality \int \, d ( \epsilon_{abcd} \omega^{ab} \wedge \theta^c \wedge \theta^...
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### Why is the refractive index for light rays travelling in circular paths proportional to $1/r$?

While studying optics, I came across a problem with solution in which the trajectory of light rays was known—circular paths around a fixed point in space, and the question was that of determining the ...
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### Finding the limiting refractive index of a rainbow

Give the limiting refractive index of a rainbow. The raindrops are modelled as spherical droplets, with refractive index $n$, with parallel rays from the Sun incident on it. I have a very limited ...
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### Confusion about breaking apart vectors

Hi I've probably got a very basic question but I'm really confused about this. If I have a vector that starts at the origin and points to say (3,-3) so the 4th quadrant, and I am wanting to split ...
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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 ...
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### 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 ...
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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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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'...
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### 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 ...
1 vote
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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 ...
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### 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 ...
488 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?
1 vote
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### 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 ...
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### 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 ...
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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 ...
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### 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 ...
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### Distance between lattice planes of a lattice with two different atoms

I know that the distance between two adjancent lattice plane of the same family is given by $$d=\frac{a}{\sqrt{h^2+k^2+l^2}}$$ if we use the conventional cell of a cube with volume $a^3$. I also know ...
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### 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 ...
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