internal geometry

Examples (10)

• In differential geometry class, we study the internal geometry of surfaces independent of how they're bent in space.
• Gauss proved that curvature is determined solely by a surface's internal geometry.
• Physicists often talk about spacetime's internal geometry rather than its visualization in higher dimensions.
• By reparameterizing the sphere, we didn't change its internal geometry.
• Two isometric embeddings share the same internal geometry.
• The theorem characterizes manifolds by their internal geometry, not by how they sit in Euclidean space.
• We measured distances along the surface to capture its internal geometry.
• Historically, non-Euclidean results arose from questioning the plane's internal geometry.
• Her paper models defects that distort the crystal's internal geometry without changing its boundary.
• Has the metric changed, or is the internal geometry essentially the same?