MathJax

Posted on March 14th, 2011 at 17:53 by John Sinteur in category: Software

If you want to do math in your web pages, check out MathJax

Here are some samples:

The Lorenz Equations

\begin{aligned} \dot{x} & = \sigma(y-x) \\ \dot{y} & = \rho x – y – xz \\ \dot{z} & = -\beta z + xy \end{aligned}

The Cauchy-Schwarz Inequality

$\left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)$

A Cross Product Formula

$\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\ \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 \end{vmatrix}$

The probability of getting $$k$$ heads when flipping $$n$$ coins is

$P(E) = {n \choose k} p^k (1-p)^{ n-k}$

An Identity of Ramanujan

$\frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} = 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} {1+\frac{e^{-8\pi}} {1+\ldots} } } }$

A Rogers-Ramanujan Identity

$1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots = \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}, \quad\quad \text{for |q|<1}.$

Maxwell’s Equations

\begin{aligned} \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\ \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\ \nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned}

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 Comments: Desiato on March 14th, 2011 at 22:37: It doesn’t work as well with NoScript running. Nik on March 17th, 2011 at 0:23: True; but NoScript does permit you to temporarily allow mathjax.org. This is great, because you get to see the original code and then the resulting visuals. Neat! I will probably never have any use for it, but certainly appreciate the effort that went into developing it.

Miyako, Japan

Posted on March 14th, 2011 at 12:48 by John Sinteur in category: Great Picture

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 Comments: Sue W on March 14th, 2011 at 15:45: For once, words fail me. Spaceman Spiff on March 14th, 2011 at 15:48: Only one thing comes to my mind – “Oh Sh!t”… John Riding on March 15th, 2011 at 10:59: This town would be my choice as a place to live in Japan; I walked through Japan 1987, and the old streets and the knifemakers shop in Miyako enchanted me straight away. I believe in the Nihonjin’s ability to weather such storms. Power to them. JR Dom on March 18th, 2011 at 18:32: I can’t even make a funny about it. Incomprehensible!

Fukushima Nuclear Accident – a simple and accurate explanation

Posted on March 14th, 2011 at 12:45 by John Sinteur in category: News

Read this before watching the news again.

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Crowley resigns as State Department spokesman

Posted on March 14th, 2011 at 10:30 by John Sinteur in category: News

[Quote]:

Sources close to the matter said the resignation, first reported by CNN, came under pressure from the White House, where officials were furious about his suggestion that the Obama administration is mistreating Manning, the Army private who is being held in solitary confinement in Quantico, Virginia, under suspicion that he leaked highly classified State Department cables to the website WikiLeaks.

Speaking to a small group at MIT last week, Crowley was asked about allegations that Manning is being tortured and kicked up a firestorm by answering that what is being done to Manning by Defense Department officials "is ridiculous and counterproductive and stupid."

So he touched a nerve, didn’t he?

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Cartoons

Posted on March 14th, 2011 at 10:13 by John Sinteur in category: Cartoon

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Japan: earthquake aftermath – The Big Picture

Posted on March 14th, 2011 at 8:43 by John Sinteur in category: Great Picture

[Quote]:

Japan raced to avert a nuclear meltdown today by flooding a nuclear reactor with seawater after Friday’s massive earthquake left more than 600 people dead and thousands more missing. Towns in the country’s northeast coast were literally wiped away by an ensuing tsunami, leaving countless people seeking shelter in the aftermath of the quake, which measured 8.9 on the Richter scale and was the country’s strongest recorded quake. — Lloyd Young 44 photos total)

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Officials in protective gear check for signs of radiation on children who are from the evacuation area near the Fukushima Daini nuclear plant in Koriyama. (Kim Kyung-Hoon/Reuters) #

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4chan hackers leak internal Bank of America emails

Posted on March 14th, 2011 at 8:26 by John Sinteur in category: Robber Barons

[Quote]:

Anonymous, a group of online hackers that frequently take up politically charged causes such as bringing down the websites for Visa and other credit card companies, has released a massive batch of internal Bank of America emails.

Mirror pt 1: http://imgur.com/1ahFt

Part 2: http://imgur.com/5v5bh

Final bit: http://imgur.com/rNZPC

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 Comments: Desiato on March 14th, 2011 at 10:33: I took a quick look but couldn’t find any deeper info yet. I’ll be curious to find out how they got the info, whether it’s the same as what WL has or whether they hacked email and got their own separate material, and more importantly, how much damaging info there is in this.