All Questions
16
questions
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Algebraic varieties associated with (simple) "string" constructions
It is relatively well-known that any arrangement of points that can be constructed with a straightedge and compass can also be constructed with an unstretchable string (of arbitrary length, negligible ...
- 131
0
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0
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32
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Constructing the optical centre point according to given conditions
If we are given the focal length value and also the distance of three collinear points ($A,B,C$ with $AB= BC= 2$ cm , $AC= 4$cm) from focal plane is given and its images from the respective focal ...
- 977
4
votes
1
answer
100
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How to obtain the bound $\lvert R_{n}(\omega)\rvert \leq \beta d(2^{n+1})^{d-1}$ in the Ising Model
From Chapter 3, page 85 of Friedli and Velenik, Statistical Mechanics of Lattice Systems: A classical mathematical introduction
https://www.unige.ch/math/folks/velenik/smbook/Ising_Model.pdf
The proof ...
- 1,838
1
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0
answers
22
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Determining valid input to this function
I've written an algorithm, the details of which I think are irrelevant here, which accomplishes the following task:
Suppose we're given three observers in a 2-dimensional plane (such that the three ...
- 1,381
11
votes
1
answer
397
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What would you see inside a spherical mirror?
Image to build a huge spherical shell made of semitransparent glass, and to cover the internal part with a reflecting material.
In such structure some light can enter, and an observer inside it (e....
user559615
3
votes
1
answer
81
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Retroreflectors in higher dimensions?
I went to an exhibition recently on the mathematics of mirrors and saw an object they called a "retroreflector", where three square mirrors are placed orthogonal to each other. The exhibit ...
- 3,285
0
votes
2
answers
1k
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Center of mass of a collection of points
We have a system of N points $(x_i, y_i)$ with masses $m_i$ and fixed distances. I want to show that there is a center of mass and derive a formula to compute its coordinates. I have argued that we ...
- 6,326
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1
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A question on the solution for the lifeguard problem (or Snell's law)
This question is about the lifeguard problem as presented on the linked assignment, essentially this is related to Snell's law. In the solution, after introducing appropriate names, the condition
$$
\...
- 18.2k
3
votes
0
answers
110
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What proportions make a regular right prism a fair dice?
If the base of a right prism is a regular $n$-gon of side 1, what height makes it a fair dice? The $n=4$ case is obvious by symmetry. Assume constant density, constant downwards gravity, throwing on a ...
- 3,388
3
votes
2
answers
1k
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How do I deal with reflections inside an ellipse?
Suppose I have an ellipse with foci $F_1$ and $F_2$. How do I show that any ray of light which intersects the segment connecting the foci will have subsequent reflections that always are tangent to ...
- 571
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votes
2
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763
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velocity confusion
A velocity encompasses both speed and direction in a single vector. I'm a little bit confused about how to separate the two.
I have 2 creatures. The first is located at position (x1, y1). The second ...
- 3
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votes
1
answer
173
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Question Concerning Magnitude And Direction Of The Accleration For Uniform Circular Motion
To find the magnitude and direction of the acclleration for the uniform circular motion,we consider the below figure
Where in particle $p$ moves at constant speed $v$ around a circle of radius $r$....
- 3,920
3
votes
1
answer
3k
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Solid body rotation around 2-axes
I am trying to understand how to describe the rotation of a solid body flying in 3D space. From physics forums, I understand that the rotation of any solid object in space, is around 2 axes ...
- 905
8
votes
2
answers
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Aren't asteroids contradicting Euler's rotation theorem?
I am totally confused about Euler's rotation theorem.
Normally I would think that an asteroid could rotate around two axes simultaneously. But Euler's rotation theorem states that:
In geometry, ...
- 905