How can one prove that the earth is a sphere (or close to it)?

Beside the Erathosthenes work, an ordinary straight line traverse 500 to 1000 kilometers long should show that your points, adjusted to sea level, will no longer be aligned in a cross section.

See #24. In what flat-earth model can you lose an entire day just by traveling?

Really, the only “proof” you need is a cell phone with GPS. If he is reasonably intelligent, ask him how the GPS timing would work for anything but a spherical Earth.

UNDENIABLE! One Simple & Fatal Flaw of the Flat Earth “Model”

While in the Navy, I spent a decent amount of time on a ship at sea. The phenomenon of seeing a distant ship “hull down” (i.e. with only its superstructure visible above the horizon), then watching the whole ship become visible as it gets closer is something encountered dozens of times a day. As distance increases, the opposite effect is noted, until all that’s visible is the very highest point on the ship, then nothing.

As you’d expect, lookouts stationed well above the water routinely see further. From a lower place, you’ll reliably see less of a distant ship (or island, or building on the shore, or anything else).
To be sure, on some days poor visibility (rain, fog, etc.) interferes with this. But in general it’s clear, apparent, obvious and unmistakable - not in any way subtle, obscure or mysterious.

Perhaps the simplest demonstration of the failure of all flat-earth models is a video of the night sky looking south in the southern hemisphere (see 1:32 in this video). You clearly see all the stars rotating around the southern celestial pole - which flat-earth models say is impossible.

The simplest demonstration that the Earth is a sphere is to get yourself a good pair of shoes and a swimsuit and start traveling in a straight line. No matter which direction you choose, you will end up back at your starting point without ever having encountered an edge.

Nah, it’s all due to refraction.
Refraction explains everything.

If you are going to rely on geometric arguments, no need to navigate all the way around the Earth. Just mark off a reasonably big triangle and sum up its angles…

In the standard flat-earth model.

Oh yeah?:

Nope. I can get the same results with a flat Earth and a Sun at an altitude of 40722 stadia (around 5000 miles)

“Always” is problematic. No one has been around to check the “always” results, and it is possible for a flat round disc to repeatedly cast a round shadow.

So in the standard flat-earth model, the earth isn’t flat but instead has a mound peaking at the North pole, to separate night from day? And to reach the edge of the Earth you just sail to Antarctica and start walking “South”?

OK. Of course when you start calculating the actual curvature parameters of this “mound”, e.g. by sailing completely around the Southern Ocean to measure the circumference there, you’ll discover … the shape is a sphere!

Just like their other arguments. At least they’re consistent. And consistently wrong.

Do you have any documented observations of a non-round Earth shadow falling across the moon? We do have centuries of well documented observations of round Earth shadows creating lunar eclipses on predictable schedules from hundreds of sources. I am content with my use of “always” in this context. If you want to present theories regarding what actually has been reliably and repeatedly observed, wonderful. Bring it on.

If things like facts and reason were going to work, these people wouldn’t be flat earthers in the first place. They’ll just invent some nonsense to explain any discrepancies in their geometry and keep on believing.

That’s why you need something like taking a trip around the world. It has to be something so overwhelmingly obvious it shakes their faith and forces them to start thinking.

I wonder how they’d explain that, a trip around the world?

No, as someone that watches way too many flat Urf videos on the YouTubes, it’s perspective!

CMC fnord!

You don’t even need a ship; a tall building with a decent overlook of flatlands or of the sea is enough. Both the Mediterranean coasts and the flatlands of Castille can provide a few such; there has to be others available in the American flatlands.