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YCor
YCor
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Smallest Trianglestriangles that Containcontain 2D Convex Regionsconvex regions with Reflection Symmetryreflection symmetry

Given any 2D convex region C$C$ with a mirror symmetry. Two pairs of questions:

  1. We need to find the smallest area (likewise, smallest perimeter) triangle that contains C$C$. Is it sufficient to only search among isosceles triangles aligned along the direction of mirror symmetry of C$C$ for answers to both questions?

  2. Similarly, if we seek the largest area (largest perimeter) triangle contained within C$C$, is it enough to look only among isosceles triangles aligned along the direction of symmetry of C$C$?

Smallest Triangles that Contain 2D Convex Regions with Reflection Symmetry

Given any 2D convex region C with a mirror symmetry. Two pairs of questions:

  1. We need to find the smallest area (likewise, smallest perimeter) triangle that contains C. Is it sufficient to only search among isosceles triangles aligned along the direction of mirror symmetry of C for answers to both questions?

  2. Similarly, if we seek the largest area (largest perimeter) triangle contained within C, is it enough to look only among isosceles triangles aligned along the direction of symmetry of C?

Smallest triangles that contain 2D convex regions with reflection symmetry

Given any 2D convex region $C$ with a mirror symmetry. Two pairs of questions:

  1. We need to find the smallest area (likewise, smallest perimeter) triangle that contains $C$. Is it sufficient to only search among isosceles triangles aligned along the direction of mirror symmetry of $C$ for answers to both questions?

  2. Similarly, if we seek the largest area (largest perimeter) triangle contained within $C$, is it enough to look only among isosceles triangles aligned along the direction of symmetry of $C$?

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Nandakumar R
Nandakumar R
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Smallest Triangles that Contain 2D Convex Regions with Reflection Symmetry

Given any 2D convex region C with a mirror symmetry. Two pairs of questions:

  1. We need to find the smallest area (likewise, smallest perimeter) triangle that contains C. Is it sufficient to only search among isosceles triangles aligned along the direction of mirror symmetry of C for answers to both questions?

  2. Similarly, if we seek the largest area (largest perimeter) triangle contained within C, is it enough to look only among isosceles triangles aligned along the direction of symmetry of C?