The geometry tag has no wiki summary.
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2answers
103 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 ...
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2answers
57 views
Limit on velocity in Minkowski Spacetime geometry
Let A be a rocket moving with velocity v.
Then the slope of its worldline in a spacetime diagram is given by c/v.
Since it is a slope, c/v = tan(theta) for some theta > 45 and theta < 90.
Does ...
3
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1answer
49 views
Uniqueness and existence of polygonal orbits through a spherical shell
Say we have a spherical wire mesh raised to a negative voltage. Then let's say we release a proton from near the surface, and away from the surface, at some angle and speed. Also, imagine that the ...
2
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2answers
63 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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3answers
548 views
Should linear algebra and vector calculus from traditional courses be replaced with `geometric algebra`?
geometric algebra gives geometric meaning to linear algebra and much more.
it can provide a coordinate free geometric interpretation of spaces.
those who learn of ...
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2answers
51 views
Where to take $\theta$ (theta) in a triangle?
This is an inclined surface having and unit vector A. The perpendicular and horizontal surfaces are the components of the inclined surface. We want to find out that how much flux will pass through ...
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2answers
78 views
How to determine Center of Gravity? [closed]
I came across this question while having conversation with one person.
We know that Center of Gravity of a solid cube is at the intersection of connecting the opposite vertex of the cube.
Suppose, you ...
1
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1answer
55 views
Rømer's determination of the speed of light
I am trying to understand Rømer's determination of the speed of light ($c$). The geometry of the situation is shown in the image below. The determination involves measuring apparent fluctuations in ...
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 ...
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0answers
49 views
Geometry for Physics [duplicate]
I am currently a high school student interested in a research career in physics. I have self taught myself single variable calculus and elementary physics upto the level of IPHO . And I am comfortable ...
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0answers
26 views
Problem in geometrical optics [duplicate]
I was trying to solve a problem taken from an Physics Olympiad when I came across a curious and complex mathematical expression. I can not prove with what I know so far about mathematics, does could ...
1
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1answer
27 views
Asking about centrepetal acceleration
please look at the fig first
1) How can you claim that the triangle ABC is same as the triangle PQR?
2) How can you claim that the angle between V1 and V2 is same as the angle between AC and AB?
...
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2answers
139 views
Calculate the center of mass of a semicircle [closed]
How I determine the center of mass of a semicircle using the definition of center of mass? I only know solve this using the Pappus theorem. Consider that the semicircle is centered on the origin and a ...
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1answer
1k views
how to calculate the angle in the x-y, y-z, x-z plane given only 3D vector direction and magnitude? [closed]
Please help me solve this. I have been thinking of all sorts of ways to solve this but can't figure out how :(. Ok here's the problem:
I am given a three dimensional velocity vector (i know the ...
0
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2answers
824 views
How do you calculate angle of projection?
At what angle the projectile should throw with initial velocity v in order to reach distance d? discard the air resistance, only gravitation acts. So far I got the equations for horizontal and ...
1
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2answers
768 views
Why do far away objects appear to move slowly in comparison to nearby objects?
When we are sitting in a moving train than nearby stationary objects appear to go backwards...in terms of physics we can use the formula
velocity of object with respect ...
4
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1answer
128 views
How is the equation of motion on an ellipse derived?
I would like to show that a particle orbiting another will follow the trajectory
\begin{equation}
r = \frac{a(1-e^2)}{1 + e \cos(\theta)}.
\end{equation}
I would like to do this with minimal ...
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0answers
45 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 ...
3
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1answer
107 views
Nanotube chiral angle as a function of $n$ and $m$
I'm looking into nanotubes and I thought I'd assure myself that the basic geometry equations are indeed correct. No problems for the radius, I quickly found the known formula:
$$R = ...
4
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1answer
95 views
Flat space metrics
This question concerns the metric of a flat space:
$$ds^2=dr^2+cr^2\,\,d\theta^2$$ where $c$ is a constant. Why is it necessary to set $c=1$ to avoid singularities and to restrict $r\ge 0$?
Thanks.
2
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2answers
107 views
Stroboscope-and-telegraph problem
Narrative:
Consider, in a suitably flat region, two straight lines which don't necessarily intersect. Let vector $\mathbf{x}$ point along one line, and vector $\mathbf{y}$ point along the other. Let ...
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1answer
259 views
Internal forces in a truss and its geometry
I'm to work out the internal forces in a truss, but I can't get my head around the geometry of the truss itself. I'm starting to think there may have been information on the diagram which I missed. ...
2
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1answer
85 views
Can we project a 4D world using 3D video technology?
Traditional movies, TV, etc, faithfully show our 3-dimensional world using 2 dimensions. So can we have a movie that shows a 4-dimensional world using 3D technology?
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11answers
749 views
Is it possible for a physical object to have a irrational length?
Suppose I have a caliper that is infinitely precise. Also suppose that this caliper returns not a number, but rather whether the precise length is rational or irrational.
If I were to use this ...
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2answers
2k views
What is the characteristic length of a cylinder
I have a cold cylinder that is submerged in hot water and I need to find the convective heat transfer coefficient. I can do the whole process but I am stuck finding the characteristic length. I found ...
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2answers
160 views
Generalized Complex Geometry and Theoretical Physics
I have been wondering about some of the different uses of Generalized Complex Geometry (GCG) in Physics. Without going into mathematical detail (see Gualtieri's thesis for reference), a Generalized ...
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2answers
202 views
Geometrical interpretation of the Dirac equation
Is there a geometrical intuitive picture behind the Dirac equation, and the gamma matrices that it uses? I know the geometric algebra is a Clifford algebra. Can the properties of geometric algebra, be ...
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. ...
4
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2answers
208 views
Space-time geometry and metric
I am confused in one question in general relativity, why we can always express a space-time geometry only by metric. It means a metric, which is just about distance in tangent space, can tell us all ...
2
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1answer
80 views
How far does typical view of clouds/atmosphere extend?
The specific "sub questions" I'm asking are:
When you are looking at clouds just on the horizon, how far away would they be?
How wide (in km) is that total field of vision at roughly cloud height.
...
2
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5answers
127 views
Why is the world sheet of an open string a cylinder?
I went to a lecture a few weeks ago and was told the following:
The world sheet of a closed string is a normal, standing cylinder.
The world sheet of an open string is a cylinder on its side.
This ...
3
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1answer
82 views
How does holographic voxel density scale with holographic film metrics?
I'm trying to understand how one can generate bounds on the effective number of voxels (volumetric pixels) in a hologram, or information density, provided various metrics for the two-dimensional ...
3
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4answers
316 views
Gravitation is not force?
Einstein said that gravity can be looked at as curvature in space- time and not as a force that is acting between bodies. (Actually what Einstein said was that gravity was curvature in space-time and ...
3
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1answer
107 views
How would one calculate the amount of water contained in a cloud?
So I was looking out the sky one day and I wondered how I would go about calculating how much water was contained in a cloud. I figured the following simple outline
1) We need to roughly know how big ...
4
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2answers
347 views
Prerequisites to start the study of noncommutative geometry in physics
What are prerequisites (in mathematics and physics), that one should know about for getting into use of ideas from noncommutative geometry in physics?
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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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1answer
220 views
Tiling hexagons on a sphere surface
In attemopt to understand basic principles of non-Euclidean geometry and its relation to physical space, I am reading General Relativity by Ben Crowell. On page 149 there is a discussion of hexagons ...
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0answers
57 views
Inscribed and Escribe Squares and Circle [closed]
Assume a circle(a) of diameter d. Inscribe a square A centred in the circle with its diagonal equal to the diameter of the circle. Now escribe a square B with the sides equal to the diameter of the ...
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4answers
667 views
What's the displacement between two opposite corners of a cube?
A cockroach is crawling along the walls inside a cubical room that has an edge length of 3 m. If the cockroach starts from the back lower left hand corner of the cube and finishes at the front ...
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4answers
154 views
Isotropy and Noise
If you have a field which value is just Gaussian noise plus a constant do you call it isotropic?
there is no preferred direction
however it is not "the same" in all directions if "the same" means ...
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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 ...
3
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1answer
160 views
Is Dyson Sphere a stable construction?
Suppose that a star is encompassed by a Dyson Sphere. Do we need a position control system for the Dyson Sphere to keep its origin always aligned with the center of the star? Will it stay aligned ...
0
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1answer
114 views
The equation of a ferrofluid under a magnetic field?
What is the parametric equation guiding the geometry of a ferrofluid under a magnetic field? See also this Wikipedia page.
From previous research, Maxwell's Equations and Navier-Stokes Equations were ...
2
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2answers
185 views
Shape of electric charges on sphere in equilibrium state
When electric charges of equal magnitude and sign are released on a regular sphere (and assume that they stick to the surface of the sphere, but they are free to move along its surface), what is the ...
2
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1answer
1k views
Determining the center of mass of a cone
I'm having some trouble with a simple classical mechanics problem, where I need to calculate the center of mass of a cone whose base radius is $a$ and height $h$..!
I know the required equation. But, ...
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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 ...
2
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1answer
180 views
Why is physical space equivalent to $\mathbb{R}^3$?
Why is physical space equivalent to $\mathbb{R}^3$, as opposed to e.g. $\mathbb{Q}^3$?
I am trying to understand what would be the logical reasons behind our assumption that our physical space is ...
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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
Can we draw a perfect circle? [closed]
Humans know the area of a circle as $\pi{r^2}$ which is an approximation for a circle of radius $r$. Can we draw a circle which is not an approximation?
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2answers
149 views
Is a semi-Euclidean space possible?
Does exists a geometry (3d for example) which is Euclidean in 2 dimensions (x and y coordinates) and non-Euclidean when the third dimension (z) is taken into account? In other words a space where it ...
