A painting is flat. Paint sits on a flat panel or a flat canvas, and yet a painted hallway can look like it recedes for thirty feet behind a wall that's really only an inch thick. That illusion isn't an accident of skilled brushwork — it's the output of a specific, checkable geometric construction, worked out and formalised in early-fifteenth-century Florence, that any painter can follow with a ruler.
The demonstration that started it
Around 1415, the architect Filippo Brunelleschi ran an experiment to prove the construction actually worked. He painted a small panel showing the Florence Baptistery exactly as seen from a specific spot just inside the cathedral doors, using the new mathematical rules to construct the receding lines. Then he drilled a small hole through the panel at the vanishing point, had a viewer look through the back of the panel at the reflection of the real Baptistery in a mirror held at arm's length in front of it, and swapped the mirror for the painting. The painted version, seen through the hole from that one exact spot, matched the reflected real building closely enough that viewers reportedly couldn't tell which one they were looking at. That was the proof: perspective wasn't a stylistic flourish, it was calculable.
One point, two points, three points, same rule
Every version of linear perspective rests on one idea: parallel lines receding away from the viewer appear, in the picture, to converge toward a shared point on the horizon called a vanishing point. One-point perspective uses a single vanishing point straight ahead — the classic view down a hallway or a railway track, where every line running "into" the picture meets at one spot. Two-point perspective, used for drawing a building corner, sends the two visible walls' lines to two separate vanishing points, one off to each side. Three-point perspective adds a third vanishing point directly above or below, for looking sharply up at a skyscraper or down from one. The construction changes with the number of points; the underlying rule — parallels converge, and the convergence point tells you exactly where the viewer is standing — never does.
What we're still unsure about
Mathematically exact linear perspective is one convention for representing depth, not the only correct one, and treating it as "how depth really looks" undersells the alternatives. Many artistic traditions — medieval European painting, much East Asian landscape painting, and others — used entirely different, deliberate systems: hierarchical scale, where importance rather than distance sets an object's size; atmospheric perspective, where distant objects simply fade and blur; oblique projection, which keeps parallel lines parallel instead of converging at all. None of these were failed attempts at Brunelleschi's geometry. They were different choices, some of them arguably more honest about the fact that a viewer has two moving eyes, not one fixed pinhole — which is exactly the assumption linear perspective quietly requires and art theorists still debate the cost of.
This sits inside Perspective (One-Point, Two-Point, Three-Point), one of seven topics in Drawing, one of five domains in Art, one of seventeen subjects the app can quiz you on.