Research demonstrates intersecting properties of spherical ellipses and triangles, suggesting new geometric insights.
For a spherical triangle ABC such that AC ̸= BC on a sphere, the circular arc(ACB and the spherical ellipse on the sphere with foci A,B that passes through C intersect in exactly two points, and the two curves cross each other at the intersection points. This fact is applied to show extremal properties for equilateral spherical triangles.
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Maehara Hiroshi (2022) studied this question.
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