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MathJax
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
\[ \begin{aligned}
\nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\
\nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\
\nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned}
\]
Miyako, Japan
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Fukushima Nuclear Accident – a simple and accurate explanation
Read this before watching the news again.
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Crowley resigns as State Department spokesman
[Quote]:
P.J. Crowley abruptly resigned Sunday as State Department spokesman over controversial comments he made about the Bradley Manning case.
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?
Cartoons
Japan: earthquake aftermath – The Big 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) #
4chan hackers leak internal Bank of America emails
[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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It doesn’t work as well with NoScript running.
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.