How Does Curvature Vary in Non-Euclidean Triangle Manifolds?

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In non-Euclidean triangle manifolds, the average curvature can be derived from the triangle's dimensions. A triangle with legs 1/a and 1/b, and hypotenuse (a²+b²)⁻¹/², presents a different curvature than its Euclidean counterpart. The discussion emphasizes the need to determine the constant curvature of this manifold. Understanding how curvature varies in these triangles is crucial for exploring geometric properties. The inquiry highlights the relationship between triangle dimensions and manifold curvature.
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A triangle with legs a and b, and hypotenuse (a2+b2)1/2, maps directly onto an Euclidean plane, of curvature zero. What is the average curvature of a manifold conformed to a triangle of legs 1/a and 1/b, and hypotenuse (a2+b2)-1/2?
 
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The above should read: "What is the constant curvature of a manifold..."
 

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