Monday, October 31, 2011

### 3-Minute Management Course

Lesson One:

An eagle was sitting on a tree resting, doing nothing.

A small rabbit saw the eagle and asked him, "Can I also sit like you and do nothing?"

The eagle answered: "Sure, why not." So, the rabbit sat on the ground below the eagle and rested.

All of a sudden, a fox appeared, jumped on the rabbit and ate it.

Management Lesson:
To be sitting and doing nothing, you must be sitting very, very high up.
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Lesson Two:

A turkey was chatting with a bull. "I would love to be able to get to the top of that tree," sighed the turkey. "But I haven't got the energy."

"Well, why don't you nibble on some of my droppings?" replied the bull. "They're packed with nutrients."

The turkey pecked at a lump of dung, and found it actually gave him enough strength to reach the lowest branch of the tree. The next day, after eating some more dung, he reached the second branch.

Finally after a fourth night, the turkey was proudly perched at the top of the tree. He was promptly spotted by a farmer, who shot him out of the tree.

Management Lesson:
Bull shit might get you to the top, but it won't keep you there.
___________________________________________________________

Lesson Three:

A little bird was flying south for the winter. It was so cold the bird froze and fell to the ground into a large field.

While he was lying there, a cow came by and dropped some dung on him.

As the frozen bird lay there in the pile of cow dung, he began to realize how warm he was. The dung was actually thawing him out! He laid there all warm and happy, and soon began to sing for joy.

A passing cat heard the bird singing and came to investigate.
Following the sound, the cat discovered the bird under the pile of cow dung, and promptly dug him out and ate him.

Management Lesson:
(1) Not everyone who shits on you is your enemy.
(2) Not everyone who gets you out of shit is your friend.
(3) And when you're in deep shit, it's best to keep your mouth shut!

This ends the three minute management course.
Saturday, October 15, 2011

### Ingenious Batman Equation

Saw this on Facebook, and I thought it's fake.

But out of curiosity, I went to google 'Batman equation", and found that somebody actually solve it!!
These people are brilliant...
And the prof who came out with this equation is genius.

Solution taken from HERE:

The ellipse (x7)2+(y3)21=0$\displaystyle \left( \frac{x}{7} \right)^{2} + \left( \frac{y}{3} \right)^{2} - 1 = 0$ looks like this:

So the curve (x7)2x3x3+(y3)2y+3337y+33371=0$\left( \frac{x}{7} \right)^{2}\sqrt{\frac{\left| \left| x \right|-3 \right|}{\left| x \right|-3}} + \left( \frac{y}{3} \right)^{2}\sqrt{\frac{\left| y+3\frac{\sqrt{33}}{7} \right|}{y+3\frac{\sqrt{33}}{7}}} - 1 = 0$ is the above ellipse, in the region where |x|>3$|x|>3$ and y>333/7$y > -3\sqrt{33}/7$:

That's the first factor.

The second factor is quite ingeniously done. The curve x2(3337)112x23+1(||x|2|1)2y=0$\left| \frac{x}{2} \right|\; -\; \frac{\left( 3\sqrt{33}-7 \right)}{112}x^{2}\; -\; 3\; +\; \sqrt{1-\left( \left| \left| x \right|-2 \right|-1 \right)^{2}}-y=0$ looks like:

This is got by adding y=x2(3337)112x23$y = \left| \frac{x}{2} \right| - \frac{\left( 3\sqrt{33}-7 \right)}{112}x^{2} - 3$, a parabola on the positive-x side, reflected:

and y=1(||x|2|1)2$y = \sqrt{1-\left( \left| \left| x \right|-2 \right|-1 \right)^{2}}$, the upper halves of the four circles (||x|2|1)2+y2=1$\left( \left| \left| x \right|-2 \right|-1 \right)^2 + y^2 = 1$:

The third factor 9((1x)(x.75))(1x)(x.75)8|x|y=0$9\sqrt{\frac{\left( \left| \left( 1-\left| x \right| \right)\left( \left| x \right|-.75 \right) \right| \right)}{\left( 1-\left| x \right| \right)\left( \left| x \right|-.75 \right)}}\; -\; 8\left| x \right|\; -\; y\; =\; 0$ is just the pair of lines y = 9 - 8|x|:

truncated to the region 0.75<|x|<1$0.75 < |x| < 1$.

Similarly, the fourth factor 3|x|+.75((.75x)(x.5)(.75x)(x.5))y=0$3\left| x \right|\; +\; .75\sqrt{\left( \frac{\left| \left( .75-\left| x \right| \right)\left( \left| x \right|-.5 \right) \right|}{\left( .75-\left| x \right| \right)\left( \left| x \right|-.5 \right)} \right)}\; -\; y\; =\; 0$ is the pair of lines y=3|x|+0.75$y = 3|x| + 0.75$:

truncated to the region 0.5<|x|<0.75$0.5 < |x| < 0.75$.

The fifth factor 2.25(.5x)(x+.5)(.5x)(x+.5)y=0$2.25\sqrt{\frac{\left| \left( .5-x \right)\left( x+.5 \right) \right|}{\left( .5-x \right)\left( x+.5 \right)}}\; -\; y\; =\; 0$ is the line y=2.25$y = 2.25$ truncated to 0.5<x<0.5$-0.5 < x < 0.5$.

Finally, 6107+(1.5.5|x|)(610)144(|x|1)2y=0$\frac{6\sqrt{10}}{7}\; +\; \left( 1.5\; -\; .5\left| x \right| \right)\; -\; \frac{\left( 6\sqrt{10} \right)}{14}\sqrt{4-\left( \left| x \right|-1 \right)^{2}}\; -\; y\; =\; 0$ looks like:

so the sixth factor 6107+(1.5.5|x|)x1x1(610)144(|x|1)2y=0$\frac{6\sqrt{10}}{7}\; +\; \left( 1.5\; -\; .5\left| x \right| \right)\sqrt{\frac{\left| \left| x \right|-1 \right|}{\left| x \right|-1}}\; -\; \frac{\left( 6\sqrt{10} \right)}{14}\sqrt{4-\left( \left| x \right|-1 \right)^{2}}\; -\; y\; =\; 0$ looks like

As a product of factors is 0$0$ iff any one of them is 0$0$, multiplying these six factors puts the curves together, giving: (the software, Grapher.app, chokes a bit on the third factor, and entirely on the fourth)