All Questions
276
questions
6
votes
2
answers
190
views
When do two triangles reflected over midpoints have the same area?
Suppose I have a triangle ABC. I have points C', A', and B' on segments AB, BC, and CA, respectively. Suppose I reflect C' about the midpoint of AB to get point C'' (also on AB); similarly for the ...
1
vote
1
answer
69
views
Calculating angle from sphere
I'm trying to calculate the angle Phi in the picture in the case where the droplet is the perfect sphere I have the correct formula but I'm not sure how they found it. and I want to know the formula ...
- 29
1
vote
1
answer
101
views
A possible new type of interference pattern?
In quantum mechanics, one often encounters complex interference patterns.
Here, I am curious about geometric interference patterns. For instance, let me define two wave-functions:
$$
\psi_1 = \exp (...
- 2,589
7
votes
0
answers
121
views
Shape of very long wire between two very tall posts (many km tall) which are attached to the earth
Consider for a moment a length of uniform wire or chain which goes between two posts of equal height. If we assume the earth to be flat then we can predict the shape of the curve using
$$y = a \cosh \...
- 181
0
votes
2
answers
432
views
How to generate random velocity vectors that can only move an object forward within a valid arc?
I have an object with known coordinates in in 3D but on the ground (z=0). The object has a direction vector. My goal is to move this object on the ground (so ...
- 435
0
votes
1
answer
55
views
Relation between force, vectors and coordinates
I have the following exercise in my math book:
A $1000\,\mathrm{kg}$ barrel hangs from a hoist. At the hoist $AC$ and $BC$ are rods and $DC$ is a steel cable. Determine the forces in the rods and the ...
- 55
5
votes
2
answers
491
views
Angle of mass hanging from two points connected at two points
I'm trying to calculate the angle (to the floor) a mass would hang if it were connected from either end to two points above it on the ceiling.
Let's call the distance between the points on the ceiling ...
1
vote
1
answer
237
views
Is there a way to find the intersection of two rectangles given their current velocity and position in constant time?
Suppose I have two rectangles, let's define them as $R_1$ and $R_2$, which each contain a length and width. Given the headings $\theta_1$ and $\theta_2$ respectively, as well as the coordinates $x_1, ...
- 11
0
votes
2
answers
69
views
equivalent function to minimize the length in curved space
Consider we have a certain metric. For instance:
\begin{equation}
ds^2 = \frac{dr^2}{r^2-Ml^2} +r^2d\phi^2.
\end{equation}
In order to find the shortest length between two angles $\phi=\alpha$ ...
- 130
2
votes
1
answer
82
views
Doubt regarding vectors in a physics question. [closed]
I thought to post this doubt in mathematics section as I thought It was more of a vector question. I haven't studied vectors but there is some use in physics. Is there any theorem from which I can get ...
- 23
4
votes
1
answer
100
views
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
vote
3
answers
110
views
Show that OC=CD
Imagine a circle with the center of O. OD is the radius of the circle. There is a line tangent to the circle at point B. AB is parallel to the radius. Point C lies on the radius. If angles ABO and OBC ...
- 59
0
votes
2
answers
457
views
Closest Two 3D Point between two Line Segment of varied Magnitude in Different Plane
Formula, Explanation And code for this is At this Link Basically This was solved in the StackOverflow question i asked...
Let's say AB1, AB2, CD1, CD2. AB1&AB2 ...
1
vote
1
answer
83
views
Find an angle to accelerate at to most quickly go from one movement vector to another
Okay, so this is with respect to game design, so that’s where I’m coming from (please try to use smol words, I am no mathematician)
I have a 2D space ship. Its velocity is defined by vector A, let’s ...
- 165
-1
votes
1
answer
39
views
Equation for area of ellipse given length of major axis and position of focus along the major axis? [closed]
I'm solving a physics question where the nearest and furthest distance of a satellite from Earth are given, along with the satellite's speed at the nearest point, and it asks to find the period of the ...
- 369