Christians are sometimes mocked for having once believed the earth was flat. However, the only references I can find are Lactantius in the beginning of the 4th century, and Copernicus, who says Lactantius was childish.
As Lactantius was largely considered a heretic throughout much of church history, is there any other reputable Christian reference to believe in a flat earth based on religious views?
Indeed, the idea that educated people in the middle ages thought the earth was flat is a myth. It was well known to have been round since well before Christ.
Many early maps represent a round earth with edges covered by a sea. It is quite possible that the earliest of these actually are meant to represent a flat earth, but that's 6th century BC.
Of course, a couple of hundred years later it was well known, at least amongst Greek philosophers, that the earth was round, and Eratosthenes calculated the earths circumference.
This didn't stop the use of maps that made the earth look like a disc, though. So called "T and O maps" was often drawn as philosophical representations of earth, throughout the middle ages. These may have helped fuel the idea that people in the middle ages thought the earth was flat, but that was not the case. These maps are just representations in principle of the earth, and should not be seen as actual maps. That also means that even the 6th century BC map above may represent a round earth.
There was attempts to make real maps fit the T and O perspective, but even so this should not be taken as a belief that the earth was flat.
They can be interpreted as representing a belief that Jerusalem was located at the "top" of the earth, and that we all lived on the "top half", something that made theological sense.
Now about the question who believed the earth was flat, the answer therefore is "not many", but of course they existed. However, the mentioned Lactantius is the one of the few who is explicit, and clearly says that a round earth makes no sense. The other two we know of are Severian of Gabala and Cosmas Indicopleustes. These two both use religious arguments and basically says the earth is flat because it makes theological sense.
John Chrysostom and Athanasius of Alexandria both expressed the idea that the earth floats on water, and this is sometimes seen as evidence that they believed in a flat world. However, these quotes are rather arguments for God as a creator, more than arguments for a flat earth, so that interpretation is somewhat more tentative.
But although some scholars seem to have argued for a flat earth from a theological standpoint, most christian scholars clearly thought the world was round.
Homilies Concerning the Statutes[75] St. John Chrysostom (344–408)
When therefore thou beholdest not a small pebble, but the whole earth borne upon the waters, and not submerged, admire the power of Him who wrought these marvellous things in a supernatural manner! And whence does this appear, that the earth is borne upon the waters? The prophet declares this when he says, "He hath founded it upon the seas, and prepared it upon the floods."1416 And again: "To him who hath founded the earth upon the waters."1417 What sayest thou? The water is not able to support a small pebble on its surface, and yet bears up the earth, great as it is; and mountains, and hills, and cities, and plants, and men, and brutes; and it is not submerged!
Similarly writes St Athanasius (c. 293 – 373): NPNF2-04. Athanasius: Select Works and Letters
Or who that sees the earth, heaviest of all things by nature, fixed upon the waters, and remaining unmoved upon what is by nature mobile, will fail to understand that there is One that has made and ordered it, even God?
Wikipedia on Flat Earth - Early Christian Church claims that these passages prove that St Athanasius and St. John Chrysostom believed in a flat earth, apparently based on their reading of Genesis 1, 9-10:
God said "Let the waters beneath the heavens gather into one place, and let dry land appear. And it was so. God named the dry land "Earth", and the gathering of waters He named "The Seas."
If so, the question is answered: We have esteemed Christian writers (saints, no less) who believed in a flat earth based on religious views. Although I am not convinced Wikipedia is correct: One can contend that they believed the earth was indeed a sphere, and balanced upon the waters, perhaps perched upon the South Pole, still Wikipedia's reading (apparently unsourced, although I did not examine all of their source material in detail), is certainly supportable from the plain meaning of those texts. See there in Wikipedia for more references on this subject.
While the observation of a ship approaching from across the horizon is a well known basis for a culture knowing that the Earth is spherical (more or less), another obvious observation is available to cultures not on a seacoast.
Any culture understanding basic geometry and capable of large scale surveying (over some miles) will notice that as a surveyed triangle gets bigger, so too does the sum of the angles of a triangle. While a small triangle on a piece of paper will have angles summing to 180 degrees with no error, if that triangle is increased in size to have its apex at one pole and its base on the equator the sum of its angles will be 180 degrees plus whatever the measured angle is at the pole - which might be as large as 180 + 179.5 = 350.5 degrees. Triangles intermediate in size will exhibit smaller discrepancies from the 180 degrees always exhibited on a flat surface. This behaviour only exists on a surface that is positively curved, such as an approximate sphere or ellipsoid. More precisely, on a rough sphere the sum of angles for a triangle can be calculated in advance from the triangle's area as a proportion of the sphere's surface area.
