Tagged Questions
2
votes
0answers
77 views
Imagining four or higher dimensions and the difference to imagining three dimensions
I’m very interested in how people envision four or higher dimensions.
And I’m especially interested in how geometers and topologists who actually work in four dimensions do.
Now I know of the video ...
11
votes
7answers
303 views
$\pi$ from the unit circle, $\sqrt 2$ from the unit square but what about $e$? [duplicate]
If one wants to introduce $\pi$ to a not mathematically savvy person, the unit circle would be a good choice. The unit square would be the way to go for $\sqrt 2$. But what about $e$? I've reviewed ...
1
vote
1answer
106 views
Kerning on the fly -algorithm [closed]
Do anyone know any algorithm which would calculate automatically kerning of characters based on glyph shapes when user types text?
I don't mean trivial calculation of advance widths or similar, I ...
2
votes
0answers
56 views
Help me to vizualise this falling ball on spinning Earth
The earth rotates. The ball falls in an latitude, not equator, let say in Germany. I am trying to understand how to express the ball in terms of the angular velocity on the planet. The constant ...
10
votes
2answers
263 views
What are all these “visualizations” of the 3-sphere?
a 2-sphere is a normal sphere. A 3-sphere is
$$
x^2 + y^2 + z^2 + w^2 = 1
$$
My first question is, why isn't the w coordinate just time? I can plot a 4-d sphere in a symbolic math program and ...
8
votes
3answers
218 views
Three-dimensional art galleries
The well-known art gallery problem starts with an "art gallery" (a simple polygon in the plane, not necessarily convex) and asks for the minimum number of "guards" (points on the polygon) required to ...
4
votes
2answers
177 views
Computing the projection of an infinite 3D grid of points
Consider the subset $S$ of $\mathbb{R}^3$ consisting of points whose coordinates are integers (compare Gaussian integers, Euclid's orchard). The view from the origin has interesting structure; it has ...
7
votes
3answers
349 views
Reconciling 'intersecting planes' and 'linear transformation' interpretations of matrices
I've learned in linear algebra class that an $n \times m$ augmented matrix can be thought of as a collection of n planes in $\mathbb {R}^m$ . If the matrix is invertible, the planes all intersect at a ...
8
votes
3answers
466 views
Is there a geometric interpretation of the exponential function of real numbers?
I can visualize the exponential function with the graph $y = e^x$, but I can do that for almost any function.
In addition to its graph, the function $f(x) = x^n$ can be visualized as the volume of a ...
