Synthesized answer
In Flatland, the concept of "solid" is contrasted with the two-dimensional existence of its inhabitants [3]. A figure from a higher dimension, when appearing in Flatland, manifests as a two-dimensional shape. For example, a Sphere appears as a Circle [1]. This Circle in Flatland is understood as a section of a three-dimensional object, composed of an infinite number of circles of varying sizes stacked one on top of the other [1].
A "Solid" is described as being constructed by a multitude of squares placed parallel to one another, stacked one upon another [2, 5]. This construction results in an object that is as high as it is long and broad, which is called a Cube [2]. To the inhabitants of Flatland, such a manifestation appears as a plane figure, and the lack of accustomed light and shade makes it difficult to perceive its true three-dimensional nature [2]. The term "Solid" is used to denote something that is not a plane figure [1].
Synthesized from the book passages below. Chat with the book on Feynman for follow-up.
From the book
atement of facts followed by ocular demonstration ought to suffice. —Now, Sir; listen to me. You are living on a Plane. What you style Flatland is the vast level surface of what I may call a fluid, or in, the top of which you and your countrymen move about, without rising above or falling below it. I am not a plane Figure, but a Solid. You call me a Circle; but in reality I am not a Circle, but an infinite number of Circles, of size varying from a Point to a Circle of thirteen inches in diameter, one placed on the top of the other. When I cut through your plane as I am now doing, I…
the other. Now a second, now a third. See, I am building up a Solid by a multitude of Squares parallel to one another. Now the Solid is complete, being as high as it is long and broad, and we call it a Cube.” [Illustration] “Pardon me, my Lord,” replied I; “but to my eye the appearance is as of an Irregular Figure whose inside is laid open to view; in other words, methinks I see no Solid, but a Plane such as we infer in Flatland; only of an Irregularity which betokens some monstrous criminal, so that the very sight of it is painful to my eyes.” “True,” said the Sphere; “it…
t because we call it so, but to make its nature clearer to you, my happy readers, who are privileged to live in Space. Imagine a vast sheet of paper on which straight Lines, Triangles, Squares, Pentagons, Hexagons, and other figures, instead of remaining fixed in their places, move freely about, on or in the surface, but without the power of rising above or sinking below it, very much like shadows—only hard with luminous edges—and you will then have a pretty correct notion of my country and countrymen. Alas, a few years ago, I should have said “my universe:” but now my mind has been…
d to denote by the word ‘upward’? I presume it is describable in the language of Flatland.” _Sphere_. Oh, certainly. It is all plain and simple, and in strict accordance with Analogy—only, by the way, you must not speak of the result as being a Figure, but as a Solid. But I will describe it to you. Or rather not I, but Analogy. We began with a single Point, which of course—being itself a Point—has only _one_ terminal Point. One Point produces a Line with _two_ terminal Points. One Line produces a Square with _four_ terminal Points. Now you can give yourself the answer to your own…
other; haply thou shalt have ample time hereafter to condole with him. Follow me.” Once more we ascended into space. “Hitherto,” said the Sphere, “I have shewn you naught save Plane Figures and their interiors. Now I must introduce you to Solids, and reveal to you the plan upon which they are constructed. Behold this multitude of moveable square cards. See, I put one on another, not, as you supposed, Northward of the other, but _on_ the other. Now a second, now a third. See, I am building up a Solid by a multitude of Squares parallel to one another.