gauss-bonnet-theorem
The chapter touches on the Gauss-Bonnet Theorem, linking total curvature and the Euler characteristic, as Yatima realizes the impossibility of flattening a sphere without curvature.
1 chapter across 1 book
Diaspora (1997)Greg Egan
In this chapter, Yatima and Radiya explore the concept of spatial curvature through immersive mathematical visualizations, focusing on the geometry of manifolds such as the torus and sphere. Yatima demonstrates how embedding a torus in four-dimensional space can yield a Euclidean geometry, but struggles with the sphere, leading to a discovery related to the Gauss-Bonnet Theorem. The chapter concludes with Yatima entering the Truth Mines, a vast indexscape containing complete mathematical proofs and axioms, highlighting the depth and accessibility of mathematical knowledge in this future setting.