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- Herausgeber: Bauer Books
- Kategorie: Für Kinder und Jugendliche
- Sprache: Englisch
- Veröffentlichungsjahr: 2021
Flatland is a mathematical essay, meant to explain a point: that higher dimensions (more than length, depth and width) may be present in our universe, but if they are, it will be nearly impossible for us to understand them.
The story itself consists of a two dimensional world (Flatland), in which there are people of assorted shapes. These shapes live regular lives, just as we do. The protagonist (a square), is visited by a sphere, which tries to explain to him the existence of a third dimension. This proves difficult, though, because to the square in flatland, the sphere appears to be nothing more than a circle that can expand, contract, disappear and reappear.
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Edwin Abbott Abbott
Table of contents
Part 1 - This World
Chapter 1 - Of the Nature of Flatland
Chapter 2 - Of the Climate and Houses in Flatland
Chapter 3 - Concerning the Inhabitants of Flatland
Chapter 4 - Concerning the Women
Chapter 5 - Of our Methods of Recognizing one another
Chapter 6 - Of Recognition by Sight
Chapter 7 - Concerning Irregular Figures
Chapter 8 - Of the Ancient Practice of Painting
Chapter 9 - Of the Universal Colour Bill
Chapter 10 - Of the Suppression of the Chromatic Sedition
Chapter 11 - Concerning our Priests
Chapter 12 - Of the Doctrine of our Priests
Part 2 - Other Worlds
Chapter 1 - How I had a Vision of Lineland
Chapter 2 - How I vainly tried to explain the nature of Flatland
Chapter 3 - Concerning a Stranger from Spaceland
Chapter 4 - How the Stranger vainly endeavoured to reveal to me in words the mysteries of Spaceland
Chapter 5 - How the Sphere, having in vain tried words, resorted to deeds
Chapter 6 - How I came to Spaceland, and what I saw there
Chapter 7 - How, though the Sphere shewed me other mysteries of Spaceland, I still desire more; and what came of it
Chapter 8 - How the Sphere encouraged me in a Vision
Chapter 9 - How I tried to teach the Theory of Three Dimensions to my Grandson, and with what success
Chapter 10 - How I then tried to diffuse the Theory of Three Dimensions by other means, and of the result
Footnotes
Table of Contents
Part 1 - This WorldChapter 1 - Of the Nature of FlatlandChapter 2 - Of the Climate and Houses in FlatlandChapter 3 - Concerning the Inhabitants of FlatlandChapter 4 - Concerning the WomenChapter 5 - Of our Methods of Recognizing one anotherChapter 6 - Of Recognition by SightChapter 7 - Concerning Irregular FiguresChapter 8 - Of the Ancient Practice of PaintingChapter 9 - Of the Universal Colour BillChapter 10 - Of the Suppression of the Chromatic SeditionChapter 11 - Concerning our PriestsChapter 12 - Of the Doctrine of our PriestsPart 2 - Other WorldsChapter 1 - How I had a Vision of LinelandChapter 2 - How I vainly tried to explain the nature of FlatlandChapter 3 - Concerning a Stranger from SpacelandChapter 4 - How the Stranger vainly endeavoured to reveal to me in words the mysteries of SpacelandChapter 5 - How the Sphere, having in vain tried words, resorted to deedsChapter 6 - How I came to Spaceland, and what I saw thereChapter 7 - How, though the Sphere shewed me other mysteries of Spaceland, I still desire more; and what came of itChapter 8 - How the Sphere encouraged me in a VisionChapter 9 - How I tried to teach the Theory of Three Dimensions to my Grandson, and with what successChapter 10 - How I then tried to diffuse the Theory of Three Dimensions by other means, and of the resultFootnotesPart 1 - This World
Part 1 This World
Chapter 1 - Of the Nature of Flatland
Chapter1 Of the Nature of Flatland
I call our world Flatland, not 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 opened to higher views of things. In such a country, you will perceive at once that it is impossible that there should be anything of what you call a "solid" kind; but I dare say you will suppose that we could at least distinguish by sight the Triangles, Squares, and other figures, moving about as I have described them. On the contrary, we could see nothing of the kind, not at least so as to distinguish one figure from another. Nothing was visible, nor could be visible, to us, except Straight Lines; and the necessity of this I will speedily demonstrate.
Place a penny on the middle of one of your tables in Space; and leaning over it, look down upon it. It will appear a circle.
But now, drawing back to the edge of the table, gradually lower your eye (thus bringing yourself more and more into the condition of the inhabitants of Flatland), and you will find the penny becoming more and more oval to your view, and at last when you have placed your eye exactly on the edge of the table (so that you are, as it were, actually a Flatlander) the penny will then have ceased to appear oval at all, and will have become, so far as you can see, a straight line.
The same thing would happen if you were to treat in the same way a Triangle, or a Square, or any other figure cut out from pasteboard. As soon as you look at it with your eye on the edge of the table, you will find that it ceases to appear to you as a figure, and that it becomes in appearance a straight line. Take for example an equilateral Triangle—who represents with us a Tradesman of the respectable class. Figure 1 represents the Tradesman as you would see him while you were bending over him from above; figures 2 and 3 represent the Tradesman, as you would see him if your eye were close to the level, or all but on the level of the table; and if your eye were quite on the level of the table (and that is how we see him in Flatland) you would see nothing but a straight line.
When I was in Spaceland I heard that your sailors have very similar experiences while they traverse your seas and discern some distant island or coast lying on the horizon. The far-off land may have bays, forelands, angles in and out to any number and extent; yet at a distance you see none of these (unless indeed your sun shines bright upon them revealing the projections and retirements by means of light and shade), nothing but a grey unbroken line upon the water.
Well, that is just what we see when one of our triangular or other acquaintances comes towards us in Flatland. As there is neither sun with us, nor any light of such a kind as to make shadows, we have none of the helps to the sight that you have in Spaceland. If our friend comes closer to us we see his line becomes larger; if he leaves us it becomes smaller; but still he looks like a straight line; be he a Triangle, Square, Pentagon, Hexagon, Circle, what you will— a straight Line he looks and nothing else.
You may perhaps ask how under these disadvantagous circumstances we are able to distinguish our friends from one another: but the answer to this very natural question will be more fitly and easily given when I come to describe the inhabitants of Flatland. For the present let me defer this subject, and say a word or two about the climate and houses in our country.
Chapter 2 - Of the Climate and Houses in Flatland
Chapter2 Of the Climate and Houses in Flatland
As with you, so also with us, there are four points of the compass North, South, East, and West.
There being no sun nor other heavenly bodies, it is impossible for us to determine the North in the usual way; but we have a method of our own. By a Law of Nature with us, there is a constant attraction to the South; and, although in temperate climates this is very slight— so that even a Woman in reasonable health can journey several furlongs northward without much difficulty— yet the hampering effort of the southward attraction is quite sufficient to serve as a compass in most parts of our earth. Moreover, the rain (which falls at stated intervals) coming always from the North, is an additional assistance; and in the towns we have the guidance of the houses, which of course have their side-walls running for the most part North and South, so that the roofs may keep off the rain from the North. In the country, where there are no houses, the trunks of the trees serve as some sort of guide. Altogether, we have not so much difficulty as might be expected in determining our bearings.
Yet in our more temperate regions, in which the southward attraction is hardly felt, walking sometimes in a perfectly desolate plain where there have been no houses nor trees to guide me, I have been occasionally compelled to remain stationary for hours together, waiting till the rain came before continuing my journey. On the weak and aged, and especially on delicate Females, the force of attraction tells much more heavily than on the robust of the Male Sex, so that it is a point of breeding, if you meet a Lady on the street, always to give her the North side of the way—by no means an easy thing to do always at short notice when you are in rude health and in a climate where it is difficult to tell your North from your South.
Windows there are none in our houses: for the light comes to us alike in our homes and out of them, by day and by night, equally at all times and in all places, whence we know not. It was in old days, with our learned men, an interesting and oft-investigate question, "What is the origin of light?" and the solution of it has been repeatedly attempted, with no other result than to crowd our lunatic asylums with the would-be solvers. Hence, after fruitless attempts to suppress such investigations indirectly by making them liable to a heavy tax, the Legislature, in comparatively recent times, absolutely prohibited them. I—alas, I alone in Flatland—know now only too well the true solution of this mysterious problem; but my knowledge cannot be made intelligible to a single one of my countrymen; and I am mocked at —I, the sole possessor of the truths of Space and of the theory of the introduction of Light from the world of three Dimensions—as if I were the maddest of the mad! But a truce to these painful digressions: let me return to our homes.
The most common form for the construction of a house is five-sided or pentagonal, as in the annexed figure. The two Northern sides RO, OF, constitute the roof, and for the most part have no doors; on the East is a small door for the Women; on the West a much larger one for the Men; the South side or floor is usually doorless.
Square and triangular houses are not allowed, and for this reason. The angles of a Square (and still more those of an equilateral Triangle,) being much more pointed than those of a Pentagon, and the lines of inanimate objects (such as houses) being dimmer than the lines of Men and Women, it follows that there is no little danger lest the points of a square of triangular house residence might do serious injury to an inconsiderate or perhaps absentminded traveller suddenly running against them: and therefore, as early as the eleventh century of our era, triangular houses were universally forbidden by Law, the only exceptions being fortifications, powder-magazines, barracks, and other state buildings, which is not desirable that the general public should approach without circumspection.
At this period, square houses were still everywhere permitted, though discouraged by a special tax. But, about three centuries afterwards, the Law decided that in all towns containing a population above ten thousand, the angle of a Pentagon was the smallest house-angle that could be allowed consistently with the public safety. The good sense of the community has seconded the efforts of the Legislature; and now, even in the country, the pentagonal construction has superseded every other. It is only now and then in some very remote and backward agricultural district that an antiquarian may still discover a square house.
Chapter 3 - Concerning the Inhabitants of Flatland
Chapter3 Concerning the Inhabitants of Flatland
The greatest length or breadth of a full grown inhabitant of Flatland may be estimated at about eleven of your inches. Twelve inches may be regarded as a maximum.
Our Women are Straight Lines.
Our Soldiers and Lowest Class of Workmen are Triangles with two equal sides, each about eleven inches long, and a base or third side so short (often not exceeding half an inch) that they form at their vertices a very sharp and formidable angle. Indeed when their bases are of the most degraded type (not more than the eighth part of an inch in size), they can hardly be distinguished from Straight lines or Women; so extremely pointed are their vertices. With us, as with you, these Triangles are distinguished from others by being called Isosceles; and by this name I shall refer to them in the following pages.
Our Middle Class consists of Equilateral or Equal-Sided Triangles.
Our Professional Men and Gentlemen are Squares (to which class I myself belong) and Five-Sided Figures or Pentagons.
