Let $(X,\mathscr T)$ be a topological space and let $a,b \in X$. A simple chain connecting $a$ and $b$ is a finite set $U_1,U_2,...,U_n$ of open sets such that $a\in U_1\setminus U_2$, $b\in U_n\setminus U_{n-1}$, and each $i,j=1,2,...,n, U_i\cap U_j \neq \emptyset$ iff $|i-j|\leq 1.$
Let $\m...
$r_{N}$ : N $\perp$ $N^{\perp}$ $\to$ N $\perp$ $N^{\perp}$
s.t $(x,y)$ $\to$ $(x,-y)$ preserves inner product of bilinear forms.
I know that $r_{N}$ . $r_{N}$= id
The Newton fractal is a boundary set in the complex plane which is characterized by Newton's method applied to a fixed polynomial
p
(
Z
)
∈
C
[
Z
]
{\displaystyle p(Z)\in \mathbb {C} [Z]}
or transcendental function. It is the Julia set of the meromorphic function
z
↦
z
−
p
(
z
)
...
Since I'm not that good at (as I like to call it) 'die-hard-mathematics', I've always liked concepts like the golden ratio or the dragon curve, which are easy to understand and explain, but are mathematically beautiful at the same time.
Do you know of any other concepts like these?
By the classical Riemann Theorem, each bounded simply-connected domain in the complex plane is the image of the unit disk under a conformal transformation, which can be illustrated drawing images of circles and radii around the center of the disk, like on this image taken from this site:
I am ...
