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Prodigi

Area of Spherical Triangles Wall Art Poster

Area of Spherical Triangles Wall Art Poster

Regular price $7.99 USD
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In spherical geometry, a "triangle" has arcs of great circles as sides. The total interior angle of a spherical triangle exceeds \(\pi\) by an amount proportional to the triangle's area. On a sphere of radius \(R\), the constant of proportionality is \(1/R^2\), the "Gaussian curvature" of the sphere. This deceptively-simple fact, a special case of the "Gauss-Bonnet theorem" in differential geometry, has profound consequences: Beings in a two-dimensional universe can define and empirically detect curvature without making reference to a higher-dimensional space. In the same sense, our own universe is curved, and the deviations from Euclidean geometry manifest to us as the force of gravity.

Printed on high-quality 170 gsm poster paper with a satin finish.

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