The "one point" in "one point perspective" isn't drawn at all, rather it is the point where all lines going into the page perpendicular to the viewing plane eventually converge to. Eg if you were to stand on a set of straight train tracks (don't do this) you would see both rails (and any roads or whatever else is parallel to them) converge to a point somewhere on the horizon line. The artists call it the "vanishing point", the mathematicians call it "the point at infinity".

Indeed with the point at infinity you can simplify geometry by dispensing with Euclid's 5th postulate. There are no parallel lines, any two lines intersect at a single point just the same way as any two points are intersected by a single line, and the intersection points of the lines we call "parallel" simply happen to be "at infinity" (outside the set of ordinary finite coordinates).

The vanishing point in a perspective drawing is a point with a value that is literally beyond the finite coordinates of any object. And you don't need to be looking at a drawing to see it.

In a certain regard its an accounting trick. Saying parallel lines meet at infinity is literally like saying "lets schedule this meeting for never", except the mathematicians added an actual box to the calendar for a date called "never" as an accounting hack, but the hack works so well you really have to wonder if it might actually be a real date or if its just an incredibly useful fiction.

Aren't all numbers just incredibly useful fictions?

Why is a date called never / a point at infinity any different?

https://i.pinimg.com/originals/20/7b/ae/207bae64d2488373fd4a...