All Questions
275
questions
4
votes
4
answers
594
views
Ray problem (geometry)
Problem:
Two plane mirrors $OP$ and $OQ$ are inclined at an acute angle (diagram is not to scale). A ray of light $XY$ parallel to $QO$ strikes mirror $OP$ at $Y$. The ray is reflected and hits ...
- 1,755
0
votes
0
answers
19
views
Computation checking: tensor contraction
I'm trying to compute $\langle dx^\mu\wedge dx^\nu, dx^\rho\wedge dx^\sigma \rangle$. This should give give the answer $G^{\mu\rho}G^{\nu\sigma}-G^{\mu\sigma}G^{\nu\rho}$, if we use the formula
$$\...
- 109
2
votes
2
answers
222
views
Is the law of reflection against math?
In my textbook of science (class 10), it is given that for any mirror, the angle of incidence is equal to the angle of reflection.
Here I m talking about spherical mirror. A convex mirror.
All rays ...
- 399
1
vote
0
answers
26
views
Is there a formal name for the shortest (directed) line segment connecting two skew lines?
Is there a formal name for the shortest (directed) line segment connecting two skew lines? I don't believe the dimension of the space matters so long as it is greater than 2. But I am specifically ...
- 3,349
0
votes
0
answers
24
views
The sum of $N-1$ cosines about an $N$-sided polygon? [duplicate]
While studying some physics problems on electrostatics, I derived this curious identity that I am having trouble proving. Show that:
$$
\sum_{n=1}^{N-1} \cos\left(\frac{2\pi{}n}{N}\right)=-1
$$
where, ...
11
votes
1
answer
481
views
Why does a wheel need seven spokes to hold it rigid? (an "inverse problem")
In the biography "King of infinite space: Donald Coxeter, the man who saved geometry" by Siobhan Roberts, the following passage describes an aspect of the subject's relationship with ...
- 1,620
2
votes
1
answer
76
views
How to calculate the center of gravity of multiple weights placed along the perimeter of a circle?
We want to attach n various weights to the perimeter of a circular turbine, equidistant from each other.
I thought about using the cosine function of the position, the weight and the radius somehow (...
- 109
0
votes
1
answer
363
views
How would I accurately simulate orbital motion in desmos? [closed]
Basically, I've been wanting to make a map of a fictional solar system which moves accurately. I have a circle to represent the parent star, a circle representing the planet, which is moving around a ...
- 111
0
votes
1
answer
37
views
The connection Between slope of two connected lines.
So I was working on a very basic physics problem that had something to do with finding the height of a triangle(the velocity vs time graph)
enter image description here
A body starts from rest with an ...
0
votes
0
answers
32
views
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
3
answers
341
views
geometrical/physical interpretation of multiplication of real numbers (including negative)
In calculus we see that the derivative has a physical interpretation as speed, and a geometric interpretation as slope, and that they are helpful when thinking intuitively about that concept. But this ...
- 27
-1
votes
2
answers
132
views
How much of the earth can see the moon? [closed]
I framed this into 2d. If you draw two circles, get the common direct tangents, then you need to find the angle between the two intersection points for the two lines and the bigger circle. Except I ...
- 83
5
votes
1
answer
796
views
Generalizing Lami's theorem
In statics, Lami's theorem is an equation relating the magnitudes of three coplanar, concurrent and non-collinear vectors, which keeps an object in static equilibrium, with the angles directly ...
- 1,011
1
vote
1
answer
75
views
Solving "when are these two exponential trajectories exactly distance ... apart"
I have two exponential functions related to a physics problem where two circles with same radius $r$ that are subject to non-linear drag travel with velocities $v_1=\{x_1,y_1\}$ and $v_2=\{x_2,y_2\}$, ...
1
vote
1
answer
631
views
What is the equation describing earth's orbit around the sun in 3 dimensional space?
I'm trying to draw a 2d ellipse in 3d space, which describes earth's orbit around the sun. such as image of a 2d ellipse in 3d space or the same image but different perspective. I'd like to be able to ...
- 11