Inversion geometry is a branch of Euclidean geometry that involves inverting points, lines, and shapes about a fixed circle or sphere. When a point is inverted, it is reflected over the circle or sphere such that the product of the distance from the point to the center of the circle before and after inversion remains constant. This creates a mirror-like transformation, but with a twist: objects closer to the center of the circle are reflected further away, and vice versa.
If we consider the Earth’s surface as the inversion circle, then every point in the universe (stars, galaxies, etc.) would have an inverted point on the inner surface of the Earth.
The geometry is quite simple. If a sphere’s center is “C” and its radius is “r,” then every outside point “P” maps to an inside point “P‘” such that “CP x CP‘ = r2“.
For any outside point “P” (on the sun, or Pluto, or Cygnus X, for example), draw a circle that has “CP” as its diameter. From one of the two points where this circle intersects the earth, draw a line perpendicular to “CP.” The intersection point {of this perpendicular and “CP“} is the location of “P‘”.
This inversion would create a perfect illusion of a ‘normal’ universe. The light from these inverted points would bend and refract due to the Earth’s atmosphere and gravitational field, creating the illusion that these celestial bodies are far away in outer space, when in fact, they are close to us on the inner surface of the Earth.
When asked if there is any way to prove we aren’t inside a hollow earth? H.S.M. Coxeter, mathematics professor at the University of Toronto and an expert on inversion geometry replied, “I can’t think of any,”. “A rocket flight, an eclipse, a Foucault pendulum, a Coriolis effect — any observation we can make on the outside of the earth has an exact duplicate version inside. There would be no way to tell which was the truth.”
Just as the geometry of space inverts, so do all the laws of physics. Toward the center of a hollow Earth, light slows down and everything shrinks — atoms, astronauts, spaceships, and measuring rods. Light travels in circular paths, producing some weird (but lawful) optical effects. Astronauts “on the moon” looked back on what they thought was a blue sphere in the distance. Actually it was the inside of the earth’s shell, through sight lines that flared like the bell of a trumpet, producing the illusion of a sphere. The optical distortion is something like the wide angle view through a fish-eye lens. As we look to the sky and the horizons, our visual field is filled with a sphere some 4,000 miles in diameter. Celestial bodies that revolve around the earth’s center appear to “rise” and “set” as they enter or leave that sphere.
It’s also worth mentioning the Australian Journal Speculations in Science and Technology published an article titled “A Geocosmos: Mapping Outer Space Into a Hollow Earth” by mathematician Mostafa A. Abdelkader, of Alexandria, Egypt, that considers in all seriousness the proposal that we really are in a hollow Earth.
