All Questions
Tagged with projective-geometry or geometry
1,053 questions
-1
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159
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Question about Earth's curvature [closed]
If the formula for the earth curvature calculator is “for every mile forward there is an 8-inch square drop”, then something 50 miles away should be roughly 1667 feet below the horizon. Is this an ...
3
votes
2
answers
234
views
Solving the Fagnano's Theorem using Hookes law and a Rubber Band
The inscribed triangle in another triangle that has the least perimeter turns out to be the orthic triangle. There is a way to prove this using absolute geometry and considering the reflections, but I ...
- 31
1
vote
1
answer
112
views
Can a floating object achieve any arbitrary submerged volume fraction by rotation if fluid density is unrestricted?
I'm studying buoyancy and am curious about how much control one has over a floating object's orientation and the fraction of its volume that lies below a fixed horizontal plane (the "waterline&...
0
votes
1
answer
200
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Doubt regarding method to find centre of mass of a cone
I was trying a certain method to find the centre of mass of the cone i.e. to prove that for a solid cone, the centre of mass is 1/4th the height from the base . This method involves cutting the cone ...
0
votes
2
answers
186
views
How are Scalar and Vector Product Different?
I have a doubt in my mind from a long time it is,
That How do we get to know that where to use the Scalar Product, and where to use Vector Product.
I have asked 3 of my collage teachers this question ...
0
votes
1
answer
105
views
Critical angle of rolling [closed]
I wondered when would a six sided polygon roll over because its COM on an incline as follows. Shouldnt it be when the line from center point to a vertex is vertical to the horizontal so half the angle ...
- 81
1
vote
0
answers
100
views
Infinite images formed by polygonal mirror
Given any convex or concave polygon whose interior sides are mirrors. And any arbitrary point inside the polygon, prove that the point forms infinite images.
So far,
In any convex polygon you can find ...
1
vote
0
answers
68
views
Translationally-invariant random metric
I am interested in applying a similarity transformation to my system in which every point in space is dilated and rotated. At first glance, I would write something like this:
$$x^i \mapsto x'^i = x^i +...
- 435
17
votes
1
answer
909
views
Is there a rigorous equivalence between the ball-on-hemisphere and falling rod problems?
These are two well-known problems in classical mechanics that yield the same critical result:
Problem 1: Ball on a Hemisphere
A small ball of mass $m$ is placed at the top of a smooth (frictionless) ...
- 273
2
votes
1
answer
264
views
Why does an angular velocity vector have an "expressed-in" frame?
$\newcommand\p[3]{{}^{#1}{p}^{#2}_{#3}} \newcommand\pdot[3]{{}^{#1}{\dot{p}}^{#2}_{#3}} \newcommand\pddot[3]{{}^{#1}{\ddot{p}}^{#2}_{#3}} \newcommand\R[2]{{}^{#1}{R}^{#2}} \newcommand\Rdot[2]{{}^{#1}{\...
- 199
0
votes
2
answers
220
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Why is focal length of a spherical mirror half of it's radius? I was trying to prove it with rules of geometry and reflection, but couldn't [closed]
Focal length is half of radius of a spherical mirror. It should be provable using geometry laws of reflection and basic ray diagram.
But even after trying with the ray diagram, I was unable to prove ...
- 11
0
votes
1
answer
131
views
How do we calculate the focus of this mirror knowing only the aperture length and the depth? [closed]
I am reading the following problem which is asking that if we know that a concave mirror is 10 inches wide and $\frac{1}{4}$ inch deep in the center (neglecting the thickness of the glass), how far ...
- 113
0
votes
0
answers
127
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Geometrical Derivation of Ball sliding off a hill
I was reading through a standard derivation of a result in a basic mechanics book that the angle at which a point mass (not rolling) leaves contact with a circular hill is given as
$$
\cos \theta = \...
- 101
11
votes
6
answers
4k
views
In light cone, why is it a cone and not a sphere, given that light travels in all directions in space-time? Is it a projection of slice of 4D sphere?
The light cone concept says that whenever a flash of light is tracked from a point in space-time, its path becomes a cone in 3d. The explanation I found is that you stack up the circle that it tracks ...
- 127
7
votes
4
answers
2k
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Doubt regarding center of mass of a cone
I would just like to confirm that if I have a solid cone of uniform density and I make a plane cut such that the 2 parts obtained have an equal mass, is it correct to state that the center of mass of ...