All Questions
32
questions
85
votes
9
answers
68k
views
What is the meaning of the third derivative of a function at a point
(Originally asked on MO by AJAY.)
What is the geometric, physical, or other meaning of the third derivative of a function at a point?
If you have interesting things to say about the meaning of the ...
- 1,133
24
votes
2
answers
5k
views
What is the exact and precise definition of an ANGLE?
On wikipedea I found a definition of an Angle as such:
"In order to measure an angle θ, a circular arc centered at the vertex of the angle is drawn, e.g. with a pair of compasses. The length of ...
- 3,989
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
17
votes
5
answers
10k
views
The vertices of an equilateral triangle are shrinking towards each other
For an equilateral triangle ABC of side $a$ vertex A is always moving in the direction of vertex B, which is always moving the direction of vertex C, which is always moving in the direction of vertex ...
- 6,799
8
votes
2
answers
2k
views
Aren't asteroids contradicting Euler's rotation theorem?
I am totally confused about Euler's rotation theorem.
Normally I would think that an asteroid could rotate around two axes simultaneously. But Euler's rotation theorem states that:
In geometry, ...
- 905
12
votes
5
answers
2k
views
Reflection inside spherical mirror
Suppose you are inside a perfectly spherical mirror. You shoot one beam of light and it reflects on the walls of the mirror. Considering the intensity is constant will the beam of light hit you again? ...
- 2,944
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
126
views
Fixing an orbit in space using r and v (Keplerian orbits)
I'm wondering what would be a good geometric method to compute orbital elements that fix the orbit in space, given that one is given the position vector $\vec{r}$ and the velocity vector $\vec{v}$ for ...
- 135
23
votes
8
answers
3k
views
What Mathematics questions can be better solved with concepts from Physics?
Over the years, I've seen several questions in mathematics that can be solved using concepts borrowed from Physics. Having seen these question, I'm interested to find out what other mathematics ...
20
votes
8
answers
4k
views
Geometrical construction for Snell's law?
Snell's law from geometrical optics states that the ratio of the angles of incidence $\theta_1$ and of the angle of refraction $\theta_2$ as shown in figure1, is the same as the opposite ratio of the ...
- 267
9
votes
1
answer
856
views
Could someone please explain sin, cos, and tan in a simple way?
I haven't taken this in school yet but I love math and physics and join lots of competitions. I have a problem with sine, cosine, and tangent, that I really need a SIMPLE explanation along with an ...
- 264
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
6
votes
2
answers
240
views
How to place optimally four electrons on a sphere?
$\newcommand{\S}{\mathbb{S}^2}$
Let $x_1,x_2,x_3,x_4 \in \mathbb{S}^2$ be points on the unit sphere, that minimizes the quantity
$$
E(x_1,x_2,x_3,x_4)=\sum_{i < j}\frac{1}{\| x_i - x_j \|},
$$
...
- 25.3k
5
votes
1
answer
981
views
Center of mass of an $n$-hemisphere
Related to this question.
Note that I'm using the geometer definition of an $n$-sphere of radius $r$, i.e.$ \\{ x \in \mathbb{R}^n : \|x\|_2 = r \\} $
Suppose I have an $n$-sphere centered at $\bf ...
- 2,580
5
votes
3
answers
1k
views
What is a geometric, physical or other meaning of the tetration?
What is a geometric, physical, or other meaning of the tetration or more high hyperoperations?
Is it exist in general or it's just a math conception?
- 1,211