Reputation
12,596
Top tag
Next privilege 15,000 Rep.
Protect questions
Badges
2 26 57
Newest
 Nice Answer
Impact
~383k people reached

Nov
20
comment Verify the polynomial of degree $≤ 4$ is exact: $\int_0^1f(x)dx ≈ {1\over90}[7f(0) + 32f({1\over 4}) + 12f({1\over 2}) + 32f({3\over 4}) + 7f(1)]$.
As a warmup, you might try to prove that $\int_0^1 f(x) \: dx = {1 \over 6} [f(0) + 4f(1/2) + f(1)]$ when $f$ is a polynomial of degree 3 or less. (This is Simpson's rule for integration.)
Nov
5
comment Show that T(n)=4×T(n−1)−T(n−2)
It would help to be more specific about the problem. What is $T$?
Nov
4
answered Simplify $\sqrt{7+4\sqrt{3}}+\sqrt{28-10\sqrt{3}}$
Oct
23
comment What is the optimal strategy in the “Factor Game”?
The fact that there's a grid doesn't matter, does it? The game plays out exactly the same on, say, a, 10-by-6 grid and a 15-by-4 grid, which both have 60 squares.
Oct
21
answered Is there any density function such that the center of mass of a semicircle about its diameter is half its radius?
Oct
16
answered Minimum number of fractions to be summed up to $\frac45$
Oct
14
comment A set of n integers is a complete residue modulo n if no two elements are congruent mod n.
This is usually called a "complete residue system", and often it's defined to be a set of $n$ integers with no two congruent mod $n$. If you've been asked to prove this, you probably have been provided some other definition of "complete residue system". What definition do you have?
Sep
28
comment How do I Approximate $\log{2}\approx 0.693$ without using the Maclaurin series?
This is Feynman's approach: feynmanlectures.caltech.edu/I_22.html
Sep
9
comment Probability that a natural number is a sum of two squares?
Perhaps also of some interest: the probability that a natural number is a sum of three squares is 5/6.
Aug
19
comment Bingo probability of a tie with 20 players
It seems very unlikely to get an answer by explicitly counting, but straightforward programming to get an answer by simulation.
Aug
9
awarded  Good Answer
Jul
29
comment Prime Numbers and a Two-Player Game
$L$ is given by oeis.org/A025043 .
Jul
22
comment asymptotics of Involutions recurrence relation
Looks like you read that section of Knuth more carefully than me. I stand corrected.
Jul
22
comment asymptotics of Involutions recurrence relation
The coefficient 7/24 is given in the reference of Knuth cited by Wimp and Zeilberger (section 5.1.4 in volume 3), but the computations are quite involved.
Jul
22
revised asymptotics of Involutions recurrence relation
[Edit removed during grace period]
Jul
21
awarded  Yearling
Jul
13
comment “Binomiable” numbers
A list of these numbers is at oeis.org/A006987 - there doesn't seem to be much there. In particular, if there were a nice criterion I'd expect it to be listed there. But it's a fun problem - keep playing around with it!
Jul
6
comment Find the parameter $m$ such that the number always be perfect square.
This solution implicitly uses the fact that $x^2 + a$ is square for all integers $x$ and only if $a = 0$. This needs a proof, although it's easy: $a^2 + a$ is not square because it's between the consecutive squares $a^2$ and $(a+1)^2$. (Note this holds even if $a$ is negative.)
Jun
22
comment Generating function solution to previous question $a_{n}=a_{\lfloor n/2\rfloor}+a_{\lfloor n/3 \rfloor}+a_{\lfloor n/6\rfloor}$
OEIS reference: oeis.org/A007731
Jun
10
reviewed Leave Open Reading list to master Numerical Analysis' research literature