## An interesting gamble

The other day I was walking on a street, along which there are a lot of booths where people play games to gamble. I...
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## VMWare Player: guest OS not full screen?

VMWare Player is a great free tool if you want to run multiple operating systems on one computer. For example, you may have a...
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## Octopus Paul, hypothesis, p-Value and significance

Null hypothesis (H0): Octopus Paul doesn’t have the ability to predict. Or, the probability that he predicts correctly on each event is 1/2. Data:...
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## Tower of sqrt(2)

What is the limit of this infinite exponential? Solution 1: $$x=\sqrt{2}^x$$ This leads to x=2 or 4 Solution 2: $$x=^x$$ This leads to x...
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## Weekly cycle of alivelearn.net traffic

Number of people visiting this blog fluctuates periodically with period 1 week. Basically on weekends few people visit.
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Basel problem: find the exact value of $$1+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+… = ?$$ Solution: We have by Taylor expansion: $$\sin(x)=x-\frac{x^3}{3!}+\frac{x^5}{5!}-\frac{x^7}{7!}+…$$ Dividing through x we have, $$\frac{\sin(x)}{x}=1-\frac{x^2}{3!}+\frac{x^4}{5!}-\frac{x^6}{7!}+…$$ Note,...
What is the value of $$i^i$$ $$i$$ being the imagery unit. This beautiful number indeed equals to $$i^i=e^{-\pi/2}=0.2079…$$