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This problem is a restatement of this question, first announced in MathStackExchange and is still unanswered after about 10 days.

We start with a triangle $T$ in the Euclidean plane and we define $A_n$ as the set of angles of the $6^n$ triangles obtained from the $n$-th barycentric subdivision of $T$. (Angles are geometric angles, i.e., the angles of $T$ and its children lie in $[0, \pi]$).

What we can say about set $A=\bigcup_{n=0}^{\infty}A_n$?

Is there a specific predefined triangle for which $A$ is dense on $(0,\pi)$?

If no, does there exist another simple alternative to this iterative procedure, i.e., barycentric subdivision, using other concurrent lines in triangles, which achieves our goal?

This problem is a restatement of this question, first announced in MathStackExchange.

We start with a triangle $T$ in the Euclidean plane and we define $A_n$ as the set of angles of the $6^n$ triangles obtained from the $n$-th barycentric subdivision of $T$. (Angles are geometric angles, i.e., the angles of $T$ and its children lie in $[0, \pi]$).

What we can say about set $A=\bigcup_{n=0}^{\infty}A_n$?

Is there a specific predefined triangle for which $A$ is dense on $(0,\pi)$?

If no, does there exist another simple alternative to this iterative procedure, i.e., barycentric subdivision, using other concurrent lines in triangles, which achieves our goal?

This problem is a restatement of this question, first announced in MathStackExchange and is still unanswered after about 10 days.

We start with a given triangle $T$ in the Euclidean plane and we define $A_n$ as the set of angles of the $6^n$ triangles obtained from the $n$-th barycentric subdivision of $T$. (Angles are geometric angles, i.e., the angles of $T$ and its children lie in $[0, \pi]$).

What we can say about set $A=\bigcup_{n=0}^{\infty}A_n$?

Is there a specific predefined triangle which $A$ is dense on $(0,\pi)$?

If no, does there exist another simple alternative to this iterative procedure, i.e., barycentric subdivision, using other concurrent lines in triangles, which achieves our goal?

This problem is a restatement of this question, first announced in MathStackExchange and is still unanswered after about 10 days.

We start with a triangle $T$ in the Euclidean plane and we define $A_n$ as the set of angles of the $6^n$ triangles obtained from the $n$-th barycentric subdivision of $T$. (Angles are geometric angles, i.e., the angles of $T$ and its children lie in $[0, \pi]$).

What we can say about set $A=\bigcup_{n=0}^{\infty}A_n$?

Is there a specific predefined triangle for which $A$ is dense on $(0,\pi)$?

If no, does there exist another simple alternative to this iterative procedure, i.e., barycentric subdivision, using other concurrent lines in triangles, which achieves our goal?

This problem is restatement of this first announced in mathexchange which is still unanswered after about 10 days.

We start with a predefined triangle $T$ on plane, first we have 3 angles of it in set $A_0$.

In $(n+1)$-th step we add angles of 6 divided triangles are made by drawing medians of triangles in $n$-th step to $A_n$ and make $A_{n+1}$.

What we can say about set $A=\bigcup_{n=0}^{\infty}A_n$?

Is there a specific predefined triangle which $A$ is dense on $(0,\pi)$?

If no  ,does there exist another simple alternative to this procedure(medians), like another defined concurance lines in triangles, which achieves our goal?

This problem is a restatement of this question, first announced in MathStackExchange and is still unanswered after about 10 days.

We start with a given triangle $T$ in the Euclidean plane and we define $A_n$ as the set of angles of the $6^n$ triangles obtained from the $n$-th barycentric subdivision of $T$. (Angles are geometric angles, i.e., the angles of $T$ and its children lie in $[0, \pi]$).

What we can say about set $A=\bigcup_{n=0}^{\infty}A_n$?

Is there a specific predefined triangle which $A$ is dense on $(0,\pi)$?

If no, does there exist another simple alternative to this iterative procedure, i.e., barycentric subdivision, using other concurrent lines in triangles, which achieves our goal?