All Questions
Tagged with euclidean-geometry algorithms
12
questions
2
votes
0
answers
250
views
Least number of circles required to cover a continuous function on $[a,b]$
I asked this question on MSE here.
Given a continuous function $f :[a,b]\to\mathbb{R}$, what is the least number of closed circles with fixed radius $r$ required to cover the graph of $f$?
It is ...
- 421
2
votes
2
answers
249
views
Procedure to determine the equality of numbers in rationals plus square root
Consider the set $\mathbb{Q}^\sqrt{}$ of real numbers that can be constructed by applying finitely many of the five operations $+$, $-$, $\cdot$, $/$ and $\sqrt{}$ to a positive rational number. ...
- 1,274
5
votes
2
answers
921
views
Automatic proof in Euclidean Geometry using Theory of Groebner Bases
I've done the same question in math.stackexchange here "https://math.stackexchange.com/questions/1938261/automatic-proof-in-euclidean-geometry-using-theory-of-groebner-bases?noredirect=1#...
- 431
4
votes
0
answers
183
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Optimal instructions for the modular construction of rectlinear Lego structures
Let $X$ be a compact (or periodic) union of integer translates of unit cubes such that the interior of $X$ is connected. (If it makes any difference, suppose that the dimension $n$ of $X$ is 3.) I am ...
- 15.3k
3
votes
1
answer
352
views
Equality of Euclidean numbers / constructible numbers
Euclidean numbers are those real number that can be constructed from the natural numbers by a finite chain of +,-,*,/ and $\sqrt{}$. They are also called Constructible Numbers.
I am now interested in ...
- 1,274
2
votes
0
answers
118
views
Containing a "fuzzy" ellipsoid within an ordinary ellipsoid
Consider the ellipsoid described by the inequality $(x - x_c)^T P^{-1} (x - x_c) \leq 1$, where the vector $x_c \in \mathbb{R}^n$ denotes the center of the ellipsoid and the symmetric positive ...
3
votes
2
answers
215
views
Equipartition of the circle [closed]
Browsing an old technical studies pupil's school book, I have found the description of a method to place at equal distance $N$ points on the circumference of a circle. I am looking for a proof of this ...
- 131
10
votes
1
answer
571
views
Can Tarski decide constructibility in elementary geometry?
Can the decision routine for Tarski's Elementary geometry be extended to decide when an existence claim in that theory can be instantiated by a compass and straightedge construction?
The answer does ...
- 10.8k
2
votes
0
answers
677
views
Find minimum-area ellipse enclosing a set of ellipses, all centered at the origin
Given a set of N > 2 (two-dimensional and coplanar) ellipses, all centered at the origin, how do I find the ellipse with the minimum area which encloses all of them?
Background:
Thanks to Will Jagy ...
- 21
6
votes
2
answers
2k
views
Find minimum-area ellipse which encloses two ellipses
I need an efficient algorithm to find the ellipse with the smallest possible area which encloses two given ellipses. The given ellipses are constrained to have coincident centers at the origin but can ...
- 61
3
votes
2
answers
622
views
Covering a sphere using reflections of an intersection of three lunes
I have been trying to figure this problem out for a while, and while I believe someone must have figured it out hundreds of years ago, I still can't quite get it.
Suppose we have a 3-dimensional ...
- 131
21
votes
8
answers
4k
views
Determine if circle is covered by some set of other circles
Suppose you have a set of circles $\mathcal{C} = \{ C_1, \ldots, C_n \}$ each with a fixed radius $r$ but varying centre coordinates. Next, you are given a new circle $C_{n+1}$ with the same radius $r$...
- 311