## fun

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 $$\sqrt{2}, \sqrt{2}^\sqrt{2}, [\s
Number of people visiting this blog fluctuates periodically with period 1 week. Basically on weekends few people visit.
Basel problem: find the exact value of $$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)}{
What is the value of $$i^i$$ \(i\) being the imagery unit. This beautiful number indeed equals to $$i^i=e^{-\pi/2}=0.2079…$$
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