Line Quotes (7)
A line is not made up of points. … In the same way, time is not made up parts considered as indivisible 'nows.'
Part of Aristotle's reply to Zeno's paradox concerning continuity.
Part of Aristotle's reply to Zeno's paradox concerning continuity.
A succinct summary, not a direct quotation of Aristotle's words. From Aristotle's Physics, Book VI. Sections 1 and 9 as given by Florian Cajori in part 2 of an article 'The History of Zeno's Arguments on Motion', in The American Mathematical Monthly (Feb 1915), 22:2, 41.
Perspective is a most subtle discovery in mathematical studies, for by means of lines it causes to appear distant that which is near, and large that which is small.
Attributed.
The course of the line we indicated as forming our grandest terrestrial fold [along the shores of Japan] returns upon itself. It is an endless fold, an endless band, the common possession of two sciences. It is geological in origin, geographical in effect. It is the wedding ring of geology and geography, uniting them at once and for ever in indissoluble union.
Presidential Address to the Geology Section, Report of the British Association for the Advancement of Science (1892), 705.
Think of the image of the world in a convex mirror. ... A well-made convex mirror of moderate aperture represents the objects in front of it as apparently solid and in fixed positions behind its surface. But the images of the distant horizon and of the sun in the sky lie behind the mirror at a limited distance, equal to its focal length. Between these and the surface of the mirror are found the images of all the other objects before it, but the images are diminished and flattened in proportion to the distance of their objects from the mirror. ... Yet every straight line or plane in the outer world is represented by a straight line or plane in the image. The image of a man measuring with a rule a straight line from the mirror, would contract more and more the farther he went, but with his shrunken rule the man in the image would count out exactly the same results as in the outer world, all lines of sight in the mirror would be represented by straight lines of sight in the mirror. In short, I do not see how men in the mirror are to discover that their bodies are not rigid solids and their experiences good examples of the correctness of Euclidean axioms. But if they could look out upon our world as we look into theirs without overstepping the boundary, they must declare it to be a picture in a spherical mirror, and would speak of us just as we speak of them; and if two inhabitants of the different worlds could communicate with one another, neither, as far as I can see, would be able to convince the other that he had the true, the other the distorted, relation. Indeed I cannot see that such a question would have any meaning at all, so long as mechanical considerations are not mixed up with it.
In 'On the Origin and Significance of Geometrical Axioms,' Popular Scientific Lectures< Second Series (1881), 57-59. In Robert Édouard Moritz, Memorabilia Mathematica (1914), 357-358.
See also: | Axiom (8) | Boundary (3) | Euclid (19) | Experience (57) | Horizon (2) | Image (4) | Inhabitant (2) | Measurement (62) | Mirror (3) | Object (13) | Solid (3) | Surface (6) | World (45)
Why are you so sure parallel lines exist?
Believe nothing, merely because you have been told it, or because it is traditional, or because you have imagined it.
Believe nothing, merely because you have been told it, or because it is traditional, or because you have imagined it.
In George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 47.
Why is geometry often described as 'cold' and 'dry?' One reason lies in its inability to describe the shape of a cloud, a mountain, coastline, or a tree. Clouds are not spheres; mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.
The Fractal Geometry of Nature (2000), xiii.
See also: | Bark (2) | Circle (3) | Cloud (6) | Cone (2) | Fractal (6) | Mountain (29) | Smooth (5) | Sphere (5)
Why is geometry often described as cold and dry? One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline, or a tree. Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line... Nature exhibits not simply a higher degree but an altogether different level of complexity.
The Fractal Geometry of Nature (1977), Introduction, xiii.
See also: | Bark (2) | Cloud (6) | Coast (3) | Complexity (18) | Cone (2) | Geometry (38) | Lightning (8) | Mountain (29) | Nature (243) | Shape (5) | Sphere (5) | Tree (18)
