# Questions tagged [geometry]

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

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### How to comprehend the fact that parity is an improper rotation in the odd dimension, but not in the even dimension, physically?

Some "clarification" To begin with, I'm not even talking about relativity so, in the following, rotations always act on the Euclidean space or only the space subpart of the Minkowski space. ...
• 111
19 views

### Find location of geo satellite [closed]

I have some satellite antenna which is installed with offset. In order to verify the offset calibration to the right direction on first installation, I'd like to instruct to the antenna the satellite ...
• 121
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### Prove dot product between two timelike vectors in Minkowski spacetimw [closed]

In the Minkowski 4-dimensional space-time $(\mathbb{M}^4,\eta)$ the dot product is: $a\cdot b = -a^0b^0 + a^1b^1 + a^2b^2 + a^3b^3 ~\qquad~ a = (a^0,a^1,a^2,a^3) ~~,~~ b = (b^0,b^1,b^2,b^3)$ Now ...
1 vote
17 views

### Force to Inflate a ball underwater [closed]

How much force is required to fully inflate (with air) a beach ball that is 6 feet in diameter at depths of 200 feet underwater?
181 views

### Are there physics theorems that can prove maths theorems? Eg Pythagoras' Theorem

There's this recent post on maths overflow Which theorems have Pythagoras' Theorem as a special case? that has an answer by dxiv that appears to use a physics theorem to a prove a maths theorem, ...
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### Please explain statement in a book on Loop Quantum Gravity

In a book by Carlo Rovelli on Covariant Loop Quantum Gravity, I struggle to understand a statement on Tetrahedron as follows: What is the dimension of the matrix? How to derive the given matrix ...
• 36
45 views

### On a minima problem in optics

I have trodding through a calculus textbook, more specifically — through a chapter on the methods of obtaining the extrema of functions using derivatives, including certain problems in optics (Fermat’...
• 101
262 views

### Why doesn’t horizon distance move exactly proportional to the height of the observer?

For instance if someone is 8 inches above the surface of the Earth, they can see approximately 1 mile to the horizon. However, if someone is viewing the horizon at an eye level of 5’5 they can only ...
49 views

### Why is the part of a sphere's area directly proportional to the square of its radius?

Solid angle in the book is explained in this way: "...Let $dA$ be a small area element of the surface of the sphere. If the points situated on the boundary of this area be joined to $O$ (the ...
123 views

### Why is the flatness problem called the "flatness" problem? What is its connection to geometry?

My understanding of the flatness problem is that it says that if we leave out dark energy and inflation, then the density parameter $\Omega(t)$ tends to $\infty$ or $0$ unless we have $\Omega(t) = 1$ ...
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### How long of a wire do i need to construct a solenoid of $N$ turns? [closed]

Consider an MRI scanner with a hole diameter of $60 ~ cm$ and producing a field of $B_{0} = 1.5 ~ T$ and has a length of $50 ~ cm$. Furthermore, let us assume that the remanence of a permanent magnet ...
• 3
177 views

### How can we define length unambiguously when measurement of length is dependent on perspective?

Suppose I have two unmarked rulers, both of same length in one perspective. Let me keep them at some place in the room , and I view them from another. In the other point of viewing, the perceived ...
• 5,281
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### How to calculate Distance $D$ to object from a camera with known $H$?

I am using algorithm to draw a bounding box around object when they appear in camera as shown in attached image. The main confusion is that i consider the object closer to camera when the Distance $D$ ...
34 views

### Geometry: path length in atmosphere ("round" Earth)

I'm having trouble obtaining this formula. I'll paste the text from the book: Considering the curvature of the Earth ($R$ is the Earth radius) and a non-vertical direction (zenith angle $θ$), the ...
• 23
30 views

### Deviation of centre of gravity when adding and subtracting shapes

Is the distance that the centre of gravity moves when adding or subtracting the same shape from another shape the same? My teacher told me to assume that circle is being added instead of subtracted ...
• 103
36 views

### Finding the uncertainty in angles that need to be changed to radians, when dealing with trigonometry ratios?

I just wanted to ask about how we are supposed to do uncertainties in our experiment since in they y-axis is acceleration/cosx and on the x axis is tanx. Are we supposed to place error bars on both ...
• 11
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### Is kinetic energy formula tightly related to Pythagoras theorem?

Consider 2 balls of mass $M$ traveling on the plain at speed $V$. One ball goes up and the other goes right. Let's associate them with the vectors $(V, 0)$ and $(0, V)$ to express their velocity and ...
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1 vote
44 views

### How did Al-Biruni know the height of a hill?

I knew of Eratosthenes famous experiment for determining the size of the Earth, but a recent question led me to read about another method by Al-Biruni. Like Eratosthenes' method, it required two ...
1k views

### How did they know the radius of the earth in ancient times?

We've all heard how in ancient times they determined that the earth was round, and were able to calculate its radius based on the measured shadows of two separate sticks in the ground at noon. I am ...
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