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Feb
2
reviewed Leave Closed Too old to start math
Feb
2
reviewed Close What's the meaning of $C^1(R)$?
Feb
2
reviewed Close Show That The Sequence $(U_n)$ Converges
Feb
2
reviewed Looks OK Show that $\hat{\theta}$ is an unbiased estimator of $\theta$
Jan
12
comment How calculators do trigonometry
A brute force approach is to do the entire computation $50000-2\pi m$ in a higher precision arithmetic.
Jan
12
comment How calculators do trigonometry
My guess is that if $mod(50000,2\pi)$ is computed internally using something like $50000-2\pi m$, then the value of $2\pi m$ is going to have an error $2m$ times the error of $\pi$. As $2m = 10^4$ roughly, the error in $x=50000-2\pi m$ would be $10^{-12}$. Such error would produce an error in $sin(x)$ of order $10^{-12}$. This seems to agree with the experimental results. In any case, the operation $50000-A$ with $50000-A\approx1$ is bound to have an error of order $10^{-12}$ just because of the cancellation of digits. So one needs to find a way without subtraction.
Jan
12
comment How does a calculator calculate the sine, cosine ,tangent using just a number?
Could one start with $x_0=1$ and then normalize in the final step?
Jan
12
comment How does a calculator calculate the sine, cosine ,tangent using just a number?
I suspect that he is talking about Chebyshev interpolation based on a precomputed table. This might be faster if the precision is predetermined.
Dec
16
comment Vanishing Gaussian curvature
I don't think $K$ will vanish in general. Why do you expect $K=0$?
Nov
14
awarded  Enlightened
Nov
14
awarded  Nice Answer
Oct
29
comment What is two-dimensional curl in terms of Stokes' theorem?
Thanks for the quick response.
Oct
29
comment What is two-dimensional curl in terms of Stokes' theorem?
Wouldn't the adjoint of the grad be -div?
Oct
13
awarded  Yearling
Sep
7
answered Picard theorem for ODE.
Sep
2
comment Regularity for a parabolic problem with nonsmooth coefficients
Do you consider accepting my answer?
Sep
1
awarded  Revival
Jun
11
comment What special role plays the function $\pi^{\frac x\pi}$ in analysis?
What is $\psi$?
Jun
7
revised Inverting a complex function
spelling
Jun
6
answered What does this definition of $C^k$ surface mean?