Astronomer, author, Authorea consultant, and developer.
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Council of 300

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'And hypnotize someone into thinking they've uploaded it and passed it around.' 'But then won't the uploader get suspicious that it pauses at 301+ for a while? Why don't we just forge the number entirel--' ::BLAM:: 'The Council of 299 is adjourned.'
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elibre
4177 days ago
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Awesome
Sydney, Australia
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3 public comments
Michdevilish
4179 days ago
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+1
Canada
adamgurri
4179 days ago
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and shall "go viral"
New York, NY
endqwerty
4179 days ago
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so who's in the council of 300 huh?
Irvine, CA
pberry
4179 days ago
I'm #57.
mithrandir
4179 days ago
Cats.
aslum
4179 days ago
If they're all watching it on the same screen, wouldn't that count as a single view?
Lythimus
4179 days ago
aslum: No, YouTube's facial recognition extends beyond the video. It counts the faces watching the video as well.
Dadster
4179 days ago
I'm with aslum that's kind of like being stopped with a case of beverages because the check-out is a "12 items or less"
bessertier
4179 days ago
if any of them are found it will promptly be the council of 298

Ramanujan approximation for circumference of an ellipse

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There’s no elementary formula for the circumference of an ellipse, but there is an elementary approximation that is extremely accurate.

An ellipse has equation (x/a)² + (y/b)² = 1. If a = b, the ellipse reduces to a circle and the circumference is simply 2πa. But the general formula for circumference requires the hypergeometric function 2F1:

\setlength\arraycolsep{1pt} \pi (a + b) \,  {}_2 F_1\left(\begin{matrix}-1/2& &-1/2 \\&1& \end{matrix}\middle;\lambda^2\right)

where λ = (ab)/(a + b).

However, if the ellipse is anywhere near circular, the following approximation due to Ramanujan is extremely good:

\pi (a + b) \left(1 + \frac{3\lambda^2}{10 + \sqrt{4 - 3\lambda^2}}\right)

To quantify what we mean by extremely good, the error is O(λ10). When an ellipse is roughly circular, λ is fairly small, and the error is on the order of λ to the 10th power.

To illustrate the accuracy of the approximation, I tried the formula out on some planets. The error increases with ellipticity, so I took the most most elliptical orbit of a planet or object formerly known as a planet. That distinction belongs to Pluto, in which case λ = 0.016. If Pluto’s orbit were exactly elliptical, you could use Ramanujan’s approximation to find the circumference of its orbit with an error less than one micrometer.

Next I tried it on something with a much more elliptical orbit: Halley’s comet. Its orbit is nearly four times longer than it is wide. For Halley’s comet, λ = 0.59 and Ramanujan’s approximation agrees with the exact result to seven significant figures. The exact result is 11,464,319,022 km and the approximation is 11,464,316,437 km.

Here’s a video showing how elliptical the comet’s orbit is.

If you’d like to experiment with the approximation, here’s some Python code:

from scipy import pi, sqrt
from scipy.special import hyp2f1

def exact(a, b):
    t = ((a-b)/(a+b))**2
    return pi*(a+b)*hyp2f1(-0.5, -0.5, 1, t)

def approx(a, b):
    t = ((a-b)/(a+b))**2
    return pi*(a+b)*(1 + 3*t/(10 + sqrt(4 - 3*t)))

# Semimajor and semiminor axes for Halley's comet orbit
a = 2.667950e9 # km
b = 6.782819e8 # km

print exact(a, b)
print approx(a, b)
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elibre
4216 days ago
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An easy way to approximate comet Haley's orbit with Python
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PEACE: Pulsar Evaluation Algorithm for Candidate Extraction -- A software package for post-analysis processing of pulsar survey candidates. (arXiv:1305.0447v1 [astro-ph.IM])

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Modern radio pulsar surveys produce a large volume of prospective candidates, the majority of which are polluted by human-created radio frequency interference or other forms of noise. Typically, large numbers of candidates need to be visually inspected in order to determine if they are real pulsars. This process can be labor intensive. In this paper, we introduce an algorithm called PEACE (Pulsar Evaluation Algorithm for Candidate Extraction) which improves the efficiency of identifying pulsar signals. The algorithm ranks the candidates based on a score function. Unlike popular machine-learning based algorithms, no prior training data sets are required. This algorithm has been applied to data from several large-scale radio pulsar surveys. Using the human-based ranking results generated by students in the Arecibo Remote Command enter programme, the statistical performance of PEACE was evaluated. It was found that PEACE ranked 68% of the student-identified pulsars within the top 0.17% of sorted candidates, 95% within the top 0.34%, and 100% within the top 3.7%. This clearly demonstrates that PEACE significantly increases the pulsar identification rate by a factor of about 50 to 1000. To date, PEACE has been directly responsible for the discovery of 47 new pulsars, 5 of which are millisecond pulsars that may be useful for pulsar timing based gravitational-wave detection projects.

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elibre
4219 days ago
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PEACE bruddah, it's times to extract your pulsars automagically
Sydney, Australia
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