All Questions
14
questions
1
vote
0
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26
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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
88
views
Calculating a building's shade with building height
I work in GIS and to create a shade layer of a building, I need to "translate" the geometry/building or permanenently move it.
But I just need some help with my formula based on this video.
...
- 101
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 ...
3
votes
3
answers
237
views
Acceleration of a ball on a plane [closed]
I have a plane ($ax+by+cz+d=0$) in a 3D world, and a gravity vector $\vec{g}$ (say it's $[0, 0, -9.81]$.) How would I find the acceleration vector of an object on this plane, ignoring friction?
- 63
1
vote
1
answer
71
views
Torque on a tetrahedron
A tetrahedron has its corners $A=(1,1,1), B=(2,0,-1), C=(0,1,-1), D=(3,1,2)$.
There is a point mass of weight $G=(0,0,-mg)$ placed on all of its corners.
What is the total torque $M$ from the weights ...
- 123
0
votes
2
answers
505
views
Ground Vehicle Handling: Is it possible to calculate the speed at which to take a turn given a turn angle and a vehicles current speed?
I'm working on AI vehicle movement for a game. This is an open terrain game so the vehicles are not using a predefined track. The AI is given a list of waypoints that they must follow believably. ...
- 3
3
votes
1
answer
81
views
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
1
answer
54
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2d Spacetime Transformations
I have a spacetime in 2-dimensions.
x is the position and t is the time.
1) t is in nanoseconds and x in feet, so the straight lines may represent 2 opposite waves that overlap and move with the ...
- 149
0
votes
2
answers
13k
views
How to prove the cross product of two vectors? [closed]
Okay, I must admit that I am lost on how to do this. I have looked up videos and tutorials about this, and they helped a little. The main thing is that my professor asked for us to solve this without ...
- 83
2
votes
0
answers
841
views
Angular moment (Hibbeler's book question)
This question's from the book HIBBELER, R. Engineering Mechanics: Statics; chapter 4.
The curved rod lies in the x-y plane and has radius $3m$. If a force $F=80N$ acts at its end as shown, determine ...
- 133
13
votes
1
answer
6k
views
Physical or geometric meaning of the trace of a matrix
The geometric meaning of the determinant of a matrix as an area or a volume is dealt with in many textbooks. However, I don't know if the trace of a matrix has a geometric meaning too.
Is there ...
- 8,294
1
vote
1
answer
116
views
Elliptical polarisation
In physic context one find the curve with parametrisation in t, $x=x_0\cos(t)$ and $y=y_0\cos(t+\varphi)$ with is an ellipse with equation
$$\left(\frac{x}{x_0\sin(\varphi)}\right)^2+\left(\frac{y}{...
- 2,790
5
votes
3
answers
3k
views
What is the relation between vectors in physics and algebra?
Vector math is something I find very interesting. However, we have never been told the link between vectors in physics (usually represented as arrows, e.g. a force vector) and in algebra (e.g. ...
- 195
6
votes
2
answers
5k
views
Prove Pythagoras theorem through dimensional analysis
I've recently become acquainted with Buckingham's Pi theorem for the first time . Then I've found an excercise that says:
Use dimensional analysis to prove the Pythagoras theorem. [Hint: Drop a ...
- 6,771