Anyone having the unfortunate experience of visiting Nathan Oakley’s YouTube channel will have seen this, or even heard it if they can stomach his bile drenched shows. The phrase is used to stop any conversation about measurement of the Earth; conversations that would otherwise show Flerfs up for the idiots they are.
Just what do they mean when they say “the Earth measures flat”?
A favourite Flerf argument is that angles have to have straight sides. Angles of celestial objects (usually the Sun) above the horizon are measured and used along with nautical almanacs to obtain one’s location on the Earth. So, the argument goes, if it’s an angle, the side that is the surface of the Earth has to be flat. No further discussion required.

It is, of course, palpable nonsense. An angle is a rotation and does not need sides. All that is required to measure the angle between, say, two stars is that they are visible; no lines needed. The only real use of lines is to help visualise the angle.
See also Curved Angles.

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