The recent surge in debate among supposedly educated people about the shape of planet Earth is surprising, considering Eratosthenes, an ancient Greek scientist, measured its circumference 22 centuries ago.

A couple of weeks spent south of the equator, much of it at sea under clear skies during which the astronomical evidence made itself obvious, sparked my own interest.

Granted, the horizon looks flat even from an airliner’s altitude. Although a geometrical argument will not prove that the earth is indeed round, it does show that a flat horizon does not rule out a curved surface.

Suppose for the moment that Earth is roughly spherical, with a circular cross section.

In geometry, a tangent is a straight line that touches (intersects with) a curve at one and only one point. The horizon is a representation of a tangent to Earth’s curved surface, the point where Earth’s surface curves so far in all directions that the surface is no longer visible.

Although the horizon appears to be a straight line, as it would be if the earth were flat, the size scale of our viewpoint is very small compared with the size of the planet. Draw or just imagine a circle the size of a 2-quart saucepan. A tangent line will appear to touch that circle at several points. For all practical purposes the difference between the straight tangent and the curved circle are the same.

Expand that scale by a factor of 17 million and you get the idea that the difference between the curved surface and a straight line is not measurable at that scale. We are very small.

The failure to see the curvature from 40,000 feet is due to that same scale difference between us humans and planet Earth.

The proof comes from a series of observations that one can make by traveling but are so common as to be available even to the nontraveler.

First, there are time zones. How can some locations be dark while others are light? It is 10 p.m. in New York when it is only 4 p.m. in Honolulu.

A flat-Earth explanation requires a great shade to cover half the earth and move with the day. When the shadow reaches the western edge, it miraculously appears on the eastern edge.

Oh, and the shadow would have to rotate around the equator by a little more than 23 degrees both ways to account for the seasonal changing of day and night lengths. What causes this?

On that same note is a reminder that the seasons are reversed in the Southern Hemisphere.

Speaking of the Southern Hemisphere, the sky is “upside down and backward” south of the equator.

The sun moves through the sky from right to left, while it still rises in the east and sets in the west. The moon is “upside down” and is on the opposite side of the sun for any given phase. Along with this is the fact that a given star or constellation changes its angle in the sky as one moves north and south.

At the equator the North Star is on the horizon. At the North Pole it is directly overhead.

Any one of these points is proof of a spheroid Earth, and to explain with a flat-Earth paradigm requires much more complex and invisible machinations than a spheroid planet. Taken together the evidence is incontrovertible.

A remaining curiosity is what exists in the human spirit that holds onto a belief despite overwhelming contrary evidence. Why do flat-Earth believers refuse to accept this evidence in favor of a demonstrably limited personal perspective?

Richard Brill is a professor of science at Honolulu Community College. His column runs on the first and third Fridays of the month. Email questions and comments to brill@hawaii.edu.