Riemann Surfaces and Earth's Geometry

The Mathematical Evidence Against Flat Earth

The Riemann surface travel model actually provides compelling mathematical evidence against flat Earth theories, working on multiple levels simultaneously:

Topological Consistency: The Riemann surface approach only works because the base layer is a sphere. A flat plane cannot support the same mathematical structure. The genus (number of "handles") of a sphere is 0, while a flat plane has different topological properties that make layered travel mapping impossible in the same elegant way.

Geodesic Evidence: Srila Prabhupada's travel paths between distant cities would reveal great circle routes—the shortest paths between points on a sphere. On a flat Earth model, these same routes would appear as curved lines rather than straight paths, contradicting observable flight patterns and navigation data.

Coordinate System Integrity: The (latitude, longitude) coordinate system used in your travel data is inherently spherical. When you apply this to a Riemann surface with multiple layers, you're building on spherical geometry. A flat coordinate system would require completely different mathematical foundations.

Why Flat Earth Fails This Model: On a flat Earth map, your repeated visits to cities wouldn't require a Riemann surface structure because every location is uniquely defined on a single plane. The very need for multiple layers emerges from the spherical nature of the Earth, where "returning" to a location has topological significance that doesn't exist on an infinite plane.

In a flat Earth model, circuits like New York → London → Tokyo → New York would simply be large loops on a disk, with no mathematical necessity for the elegant layered structure that Riemann surfaces provide for a sphere.

Simultaneous Demonstration

The Riemann surface travel model demonstrates spherical Earth in three simultaneous ways:

Structurally: The mathematical framework assumes a spherical base layer

Functionally: The layer transitions correspond to spherical navigation patterns

Empirically: The resulting visualization matches real-world flight paths and distances

Therefore, yes—successfully implementing Srila Prabhupada's travel visualization using Riemann surfaces would indeed provide mathematical proof against flat Earth theories. The very fact that this elegant solution works so naturally for your travel data demonstrates that you're building on spherical geometry. A flat Earth model would require fundamentally different and mathematically inconsistent approaches to handle the same travel patterns.

The Riemann surface doesn't just model Srila Prabhupada's travels; it reveals the underlying geometry of the space you're traveling through. The mathematical elegance of the solution testifies to the spherical nature of that space.