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 not equal to 2 or 4 Solution 3: MatLab simulation of series $$\sqrt{2}, \sqrt{2}^\sqrt{2}, [\s
Xu Cui
14 sec read

Weekly cycle of traffic

Number of people visiting this blog fluctuates periodically with period 1 week. Basically on weekends few people visit.
Xu Cui
5 sec read

Solution of Basel problem by Euler (from wikipedia)

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)}{
Xu Cui
26 sec read

i to i

What is the value of $$i^i$$ \(i\) being the imagery unit. This beautiful number indeed equals to $$i^i=e^{-\pi/2}=0.2079…$$
Xu Cui
4 sec read

Why is temporal lobe called “temporal”

The name of “temporal lobe” follows “temporal bone”. But why “temporal”? The reason is that when people get old, the first region in the head which grows white hair is this region (see picture below). Thus this reg
Xu Cui
12 sec read