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Oct
29
awarded  Teacher
Oct
21
answered Is there a map from a segment to a triangle?
Oct
14
comment Is there a map from a segment to a triangle?
Thank you very much for help! By the way, doest it follow, that diameters of the circle go to straight lines in hexagon from your argument?
Oct
13
awarded  Supporter
Oct
13
comment Is there a map from a segment to a triangle?
I would like to precise the argument via symmetry principle: so, I do have a map from the unit circle to a hexagon. Let me now choose a point that maps to a vertice, and a corresponding diameter of a unit circle. Why does this diameter map to a line connecting edges of hexagon? Because only in this case we can apply symmetry principle.
Oct
13
comment Is there a map from a segment to a triangle?
Do I understand correctly that I actually can choose $Arg f'(0)$ to be any angle I want (by Riemann theorem construction) and that determines my map? And as far as I understand, for any choice of $Arg f'(0)$ the map will still map vertices to vertices, isn't it?
Oct
13
comment Is there a map from a segment to a triangle?
Yes, I do want a conformal mapping of interiors, without boundary.
Oct
13
awarded  Editor
Oct
13
comment Is there a map from a segment to a triangle?
Many thanks for your answer but I've forgotten the most important point - the "vertices" should map to vertices. I've changed the question.
Oct
13
revised Is there a map from a segment to a triangle?
added 84 characters in body
Oct
13
awarded  Student
Oct
13
asked Is there a map from a segment to a triangle?