A common way to visualize the proof is by "flattening" a polyhedron:
The formula is significant because it marks the birth of . Unlike geometry, which cares about lengths and angles, topology cares about how a shape is connected. No matter how much you stretch or deform a cube (as long as you don't tear it), the result of will always equal 2. Euler's Gem
Remove one face of a polyhedron (like a cube) and stretch the remaining shell flat onto a plane. A common way to visualize the proof is
Ensuring 3D meshes are "manifold" (water-tight). which cares about lengths and angles
The "2" in the formula represents the "internal" connectivity and the "external" face that was removed.
