It seems that *Mark J.Nielsen* have solved this problem [here][1] that I have found it recently, where he was proved this theorem about inscribed triangles in closed simple jordan curves:

**[Theorem E][2]:** *Extending Theorem D, J has so many inscribed triangles similar to T that the vertices of all these inscribed triangles are "dense" in the curve J.*

As the article needs license I do not have access to the whole solution ,I think it would be great to present and discuss about the way the problem has been solved Here.


  [1]: http://Extending%20Theorem%20D,%20J%20has%20so%20many%20inscribed%20triangles%20similar%20to%20T%20that%20the%20vertices%20of%20all%20these%20inscribed%20triangles%20are%20%22dense%22%20in%20the%20curve%20J.
  [2]: http://www.webpages.uidaho.edu/~markn/squares/