3
votes
1answer
160 views

bounding the probability that a polynomial is near 0

Given a polynomial $p(x_1,\ldots, x_k)$ in $k$ variables with maximum degree $n$, and $x_1,\ldots, x_k \in [0,1]$. Suppose $\max_{x \in [0,1]^k} p(x) = 1$, can we get an upper bound on the probability ...
2
votes
1answer
312 views

Complexity of computing derivatives

Sorry if this is too simple. This is my first question here. Suppose $f : R^n \to R$ is a differentiable function. Say that we can compute in $T$ arithmetic operations the value $f(x)$ at any point ...
13
votes
5answers
1k views

Characterizing visual proofs

``Proofs without words'' is a popular column in the Mathematics magazine. Question: What would be a nice way to characterize which assertions have such visual proofs? What definitions would one ...
2
votes
0answers
258 views

Drawing a combinatorial 3-configuration of points and lines with pseudolines

This question is related to the question of drawing a combinatorial 3-configuration of points and lines with straight lines. We only relax the condition and admit drawings with pseudolines. Let us ...
11
votes
2answers
604 views

Drawing 3-configurations of points and lines with straight lines

It is well-known that the black-and-white coloring of the Heawood graph on 14 vertices determines a combinatorial 3-configuration with 7 "points" and 7 "lines", known as Fano plane. Similarly, any ...