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 museum-quality fine art print paper (200 gsm) with a textured, matte finish.
