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Apr
12
comment Relation between mean width and diameter
Consider this argument: Let L be the line segment connecting the two farthest points in A. Its length is the diameter. Now construct two hyperplanes perpendicular two it at its endpoints. By definition of L, no point in A can lie beyond the hyperplanes, therefore it is also the maximal width.
Apr
12
comment Relation between mean width and diameter
Aren't they equal in the case of a compact set? Or at least compact and convex?
Apr
10
comment Relation between mean width and diameter
Excellent answer! Thank you very much :)
Apr
10
accepted Relation between mean width and diameter
Apr
10
asked Relation between mean width and diameter
Apr
7
answered What is $\cos(k \pi)$?
Apr
5
revised Primes related to the structure $\left| \pm a\pm b\pm c \right| $
changed math in title to be inline
Apr
5
revised Where is my mistake?
edited tags
Apr
5
answered Where is my mistake?
Apr
1
comment Why is cosine a sine function with offset pi/2?
This is basically the same as Michael T's answer, who submitted it first :)
Apr
1
answered Why is cosine a sine function with offset pi/2?
Apr
1
answered Evaluating $\int_0^{2 \pi} \sin^4 \theta\: \mathrm{d} \theta$
Mar
31
comment Examples of mathematical results discovered “late”
Yes, this was a big surprise :) I don't know if it was more surprising that it was independent of RH than that it was elementary.
Mar
31
answered Limit of $1+ \frac13 + \frac15 + … + \frac{1}{2n+1} -2 \ln n $
Mar
30
comment Examples of mathematical results discovered “late”
Looked up what I wrote in the previous comment, I made a mistake. It's not called "Ankeny's algorithm", it's simply the Euler-Jacobi test. Ankeny's theorem (1950s) guarantees (conditional GRH) that if $n$ is composite then there is a base $a < 2(\log n)^2$ for which $n$ is not an Euler-Jacobi pseudoprime, which yields a trivial polynomial time algorithm (check all bases $a$ up to $2(\log n)^2$...)
Mar
30
comment Examples of mathematical results discovered “late”
I think it is a misconception that "it was the common belief that PRIMES is not in P". It was actually known in the 1980s that if the Generalized Riemann Hypothesis is true then PRIMES is in P (via the not-as-well-known Ankeny's algorithm). Since many people believe GRH, it was believed that PRIMES is in P. The new result of AKS in 2002 is a proof that doesn't depend on GRH.
Mar
29
awarded  Benefactor
Mar
29
comment Sum of squares function usually larger than $(\log x)^{1/2 - \epsilon}$?
Thanks! Very interesting analysis :)
Mar
26
comment Sum of squares function usually larger than $(\log x)^{1/2 - \epsilon}$?
Thank you! This helps a lot!
Mar
18
answered Why is variance squared?