I know that iterating the following incircle construction approaches an equilateral triangle in the limit:
Starting with any triangle $T$, one forms $T'$ by connecting the three points
of tangency of the circle inscribed inside $T$.
Does the analogous process for tetrahedra approach a regular tetrahedron? And the same question may be asked for simplices in $\mathbb{R}^d$. A reference would be appreciated—Thanks!
I know that iterating the following incircle construction approaches an equilateral triangle in the limit:
Starting with any triangle $T$, one forms $T'$ by connecting the three points
of tangency of the circle inscribed inside $T$.
Does the analogous process for tetrahedra approach a regular tetrahedron? And the same question may be asked for simplices in $\mathbb{R}^d$. A reference would be appreciated—Thanks!
I know that iterating the following incircle construction approaches an equilateral triangle in the limit:
Starting with any triangle $T$, one forms $T'$ by connecting the three points
of tangency of the circle inscribed inside $T$.
Does the analogous process for tetrahedra approach a regular tetrahedron? And the same question may be asked for simplices in $\mathbb{R}^d$. A reference would be appreciated—Thanks!
I know that iterating the following incircle construction approaches an equilateral triangle in the limit:
Starting with any triangle $T$, one forms $T'$ by connecting the three points
of tangency of the incircle tocircle inscribed inside $T$.
Does the analogous process for tetrahedra approach a regular tetrahedron? And the same question may be asked for simplices in $\mathbb{R}^d$. A reference would be appreciated—Thanks!
I know that iterating the following incircle construction approaches an equilateral triangle in the limit:
Starting with any triangle $T$, one forms $T'$ by connecting the three points
of tangency of the incircle to $T$.
Does the analogous process for tetrahedra approach a regular tetrahedron? And the same question may be asked for simplices in $\mathbb{R}^d$. A reference would be appreciated—Thanks!
I know that iterating the following incircle construction approaches an equilateral triangle in the limit:
Starting with any triangle $T$, one forms $T'$ by connecting the three points
of tangency of the circle inscribed inside $T$.
Does the analogous process for tetrahedra approach a regular tetrahedron? And the same question may be asked for simplices in $\mathbb{R}^d$. A reference would be appreciated—Thanks!
