All Questions
276
questions
85
votes
9
answers
68k
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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
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
19
votes
4
answers
608
views
A simple geometric problem, solving $f'(x)=\frac{f(x)}{\sqrt{r(x)^2-f(x)^2}}$, given $r(x)$.
Introduction
Suppose we have a convex, real function $f(x)$. We can define a tangent line to this function $t(x,s)$. Then, we can find the intersection of $t(x,s)$ with the $x$ axis. Let's call this ...
18
votes
3
answers
798
views
What is the moment of inertia of a Gosper island?
We know that regular hexagons can tile the plane but not in a self-similar fashion. However we can construct a fractal known as a Gosper island, that has the same area as the hexagon but has the ...
- 4,183
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
15
votes
5
answers
6k
views
Help to identify every equation in this meme? [closed]
A couple of the equations in this meme aren’t easy to read, and I probably don’t know them so I couldn’t tell what they are.
Can you identify all the equations, and help me feel smart on twitter?
- 839
13
votes
2
answers
276
views
Is it possible to use physics or other form of non-canonical reasoning to study functions?
It is well-known (see, for example, the books New Horizons in geometry, Maxima and minima without calculus and The Mathematical Mechanic) that it is possible to use some forms of "physical reasoning", ...
- 8,294
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
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
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
11
votes
1
answer
397
views
What would you see inside a spherical mirror?
Image to build a huge spherical shell made of semitransparent glass, and to cover the internal part with a reflecting material.
In such structure some light can enter, and an observer inside it (e....
user559615
10
votes
1
answer
2k
views
What Is the Hardest Shape To Roll?
I was having a discussion with a friend about rolling various shapes, in particular what shape is the worst at rolling. I thought that a triangular wheel might be particularly bad at rolling while he ...
- 2,258
10
votes
1
answer
1k
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Does apparent retrograde motion of planets begin and end at quadrature?
I've read it several places that the apparent retrograde motion of planets (during which they seem, as viewed from Earth, to move in the opposite sense of their normal "direct" orbital motion against ...
- 2,371