Eratosthenes' experiment could just as easily prove a smaller, closer sun

The best proof is that you can look at the Sun and the moon with your eyes (maybe use a filter for the sun) and see them not change size throughout their path along the sky, which proves that they aren't getting appreciably closer or farther

What do Eratosthenes' proclivities have to do with astronomy

There was this one video where flat-Earthers tried to prove the Earth was flat, so they recreated the experiment by Eratosthenes and accidentally proved the Earth was round. I can't find it right now but it's hilarious.

Flat earthers: "We only believe what we can see for ourselves!"

Also flat earthers: "And then there is a great ice wall around it and then there are other earths just like ours in other pockets like that"

Explanation: Not only did the ancient Greek philosopher Eratosthenes (born and raised in what-is-now Libya) know the earth was spherical, he used that knowledge to measure the circumference of the earth - with two sticks and some carefully applied mathematical thought - to an astounding accuracy!

According to Cleomedes' On the Circular Motions of the Celestial Bodies, around 240 BC, Eratosthenes calculated the circumference of the Earth in Ptolemaic Egypt.[8] Using a vertical rod known as a gnomon and under the previous assumptions, he knew that at local noon on the summer solstice in Syene (modern Aswan, Egypt), the Sun was directly overhead, as the gnomon cast no shadow. Additionally, the shadow of someone looking down a deep well at that time in Syene blocked the reflection of the Sun on the water. Eratosthenes then measured the Sun's angle of elevation at noon in Alexandria by measuring the length of another gnomon's shadow on the ground.[9] Using the length of the rod and the length of the shadow as the legs of a triangle, he calculated the angle of the sun's rays.[10] This angle was about 7°, or 1/50th the circumference of a circle; assuming the Earth to be perfectly spherical, he concluded that its circumference was 50 times the known distance from Alexandria to Syene (5,000 stadia, a figure that was checked yearly), i.e. 250,000 stadia.[11] Depending on whether he used the "Olympic stade" (176.4 m) or the Italian stade (184.8 m), this would imply a circumference of 44,100 km (an error of 10%) or 46,100 km, an error of 15%.[11] A value for the stadion of 157.7 metres has even been posited by L.V. Firsov, which would give an even better precision, but is plagued by calculation errors and false assumptions.[12] In 2012, Anthony Abreu Mora repeated Eratosthenes's calculation with more accurate data; the result was 40,074 km, which is 66 km different (0.16%) from the currently accepted polar circumference.[10]

I talked to a guy that worked in one of the deepest underground mines in Kirkland Lake, Ontario. He said one of his bosses, a highly educated libertarian nut job was a flat earther and would debate his workers on a regular basis about it. I told him they should ask for more danger pay because at one point they might drill through the flat earth plain and fall into space .... or land on a turtle.

small voice Oblate spheroid.

We can't prove in a way that they would believe.

Oh, let's be fair here...

He had to hire a guy to count lots and lots of steps too.

Of course it's not spherical, it's wider at the equator and lumpy

Eratosthenes is a word I can only hear in Carl Sagan's voice.

They also can't prove for sure that the earth is flat

But the earth is round, like a pizza