jordan curve and koch curve How to I prove that koch curve is jordan curve? I want to find continious parametric equation of koch curve. Or is there another way to prove koch curve is jordan curve
 A: The Koch curve is described recursively, starting with relatively simple curves and building more complicated ones, and taking the limit. You may try to come up with parametric equations for each of the simpler curves, then take limit of these functions and use that the (uniform) limit of the sequence of these functions is continuous, and represents the Koch curve. 
The above is what I would think is the main idea. But I googled it and found out that something like this has already been done (I would guess perhaps more than once), but here is one link. 
The taming of a monster: a parametrization of the von Koch Curve,
Hans Sagan
International Journal of Mathematical Education in Science and Technology
Volume 25, 1994, Issue 6, Pages 869-877
Received 02 Jun 1993, Published online: 09 Jul 2006
https://www.tandfonline.com/doi/abs/10.1080/0020739940250612?journalCode=tmes20
https://doi.org/10.1080/0020739940250612
Following a brief historical introduction, the iterated function system, consisting of four similarity transformations, that has the von Koch curve as invariant attractor set, is utilized to parametrize that curve with the parameter in quaternary form. The resulting parameter representation lends itself readily to evaluation by computer.
There is also a book by the same author. 
Space-Filling Curves,
By Hans Sagan
Edit. Also as an additional comment, the Koch curve is self-similar, and a first example of this type was the Peano space-filling curve, also self-similar (though Koch's curve is not as "thick"). 
There is a parametrization for the Peano curve, that is how it was introduced to begin with, see: 
G. Peano,
"Sur une courbe, qui remplit toute une aire plane",
Mathematische Annalen 36 (1): 157–160. (1890).
http://www.digizeitschriften.de/dms/img/?PID=GDZPPN002252376
I used this parametrization once to generate computer code, and approximations to the Peano curve:
https://www.youtube.com/watch?v=MaoCp08hznM
see the description there for more online links to Peano's paper.  
