Let’s suppose that we have some kind of special 3-dimensional rotating automaton. The automaton is capable to generate rotation about selected $X$ or $Y$ or $Z$ axis (in a current frame) in steps by only constant +$\dfrac{\pi}{6}$ angle (i.e. rotation can be generated only in one direction – reverse rotation is prohibited) so transition from […]

Take $1$ step forward, turn $90$ degrees to the left, take $1$ step forward, turn $90$ degrees to the left … and keep going, alternating a step forward and a $90$-degree turn to the left. Where do you end up walking? It’s very easy to see that you end up walking on the perimeter of […]

Intereting Posts

“Where” exactly are complex numbers used “in the real world”?
How could I improve this approximation?
For every $n < \omega$, $\aleph_n^{\aleph_0} = \max(\aleph_n,\aleph_0^{\aleph_0})$
Why $\sqrt{-1 \times -1} \neq \sqrt{-1}^2$?
$X$ compact metric space, $f:X\rightarrow\mathbb{R}$ continuous attains max/min
What is the difference between projected gradient descent and ordinary gradient descent?
How many ways to arrange m chosen objects when there are n total objects, and some are indistinguishable?
Explicit formula of Mobius Transformation that maps non intersecting circles to concentric circles
Description of SU(1, 1)
Can permutating the digits of an irrational/transcendental number give any other such number?
Properties of $||f||_{\infty}$ – the infinity norm
Show that $\sum_{n=1}^\infty \frac{n^2}{(n+1)!}=e-1$
Better representaion of natural numbers as sets?
“completing the cube”
Evaluate the integral $\int_0^{\infty} \left(\frac{\log x \arctan x}{x}\right)^2 \ dx$