The geometry tag has no wiki summary.
2
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2answers
64 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 ...
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2answers
105 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 ...
1
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1answer
61 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 ...
2
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0answers
49 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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0answers
93 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. ...
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0answers
90 views
How far is the horizon, if a 2m tall man watches to the sea?
How far is the horizon, if a $r=2 m$ tall man watches to the sea?
I have calculated that it would be even just about 6 km. if R = radius of earth( $6370 \cdot10^3$ m ).
By pythagorean theorem we ...
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0answers
80 views
Self-organizing maps
I'm currently interested in this subject but all I can see is about neural networks and I'm more interested on the Theoretical point of view: "how can a system (Lagrangian/Hamiltonian) alter it's ...
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0answers
46 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 ...
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0answers
129 views
Motions in Non-inertial reference frames? Reference -request
The course 0.2061 in Aalto University covers motion in non-inertial-reference frame but without examples and without references (examples are outlined only in lectures but I find them very hard to ...
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0answers
76 views
Searching for clues on “spacelike”-ness by “impossible figures”
Remark on version (3):
In the first version of my question main text the already lengthy "logic statement" -- let's call it "paradigm statement" in the following -- involved conditions on only 24 ...
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0answers
94 views
Does the measure of proximity of two theories in “theory space” run?
From reading this article, I have learned that two effective QFTs can be very close together in the "theory space" appropriate to describe for example physics at the LHC scale, whereas the ...
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170 views
Extrinsic curvature versus Intrinsic curvature (Euclidean versus Riemannian)
Do we believe the universe has any extrinsic curvature at all? As far as I'm aware extrinsic curvature is only used in geometry/math to model the intrinsic curvature, correct?
From the answers to ...
