Quotes & Sayings About Lines In Geometry

Regular geometry, the geometry of Euclid, is concerned with shapes which are smooth, except perhaps for corners and lines, special lines which are singularities, but some shapes in nature are so complicated that they are equally complicated at the big scale and come closer and closer and they don't become any less complicated. — Benoit Mandelbrot

[In comedy] you never want to leave the actors hanging out to dry. So you need to come up with funny individual stories for each character, and then you do this sort of comedy geometry, weaving them together. Once you've got a funny structure and you know why the scenes are funny, then you get super funny people to say your own lines, say their own lines, say things in their own way, and every scene is a live rewrite in front of the camera. — Jeff Schaffer

Free will is an idealization of human beings that makes the ethics game playable. Euclidean geometry requires idealizations like infinite straight lines and perfect circles, and its deductions are sound and useful even though the world does not really have infinite straight lines or perfect circles. The world is close enough to the idealization that the theorems can usefully be applied. Similarly, ethical theory requires idealizations like free, sentient, rational, equivalent agents whose behavior is uncaused, and its conclusions can be sound and useful even though the world, as seen by science, does not really have uncaused events. As long as there is no outright coercion or gross malfunction of reasoning, the world is close enough to the idealization of free will that moral theory can meaningfully be applied to it. — Steven Pinker

The classical theorists resemble Euclidean geometers in a non-Euclidean world who, discovering that in experience straight lines apparently parallel often meet, rebuke the lines for not keeping straight as the only remedy for the unfortunate collisions which are occurring. Yet, in truth, there is no remedy except to throw over the axiom of parallels and to work out a non-Euclidean geometry. — John Maynard Keynes

Believe me, if Archimedes ever had the grand entrance of a girl as pretty as Gloria to look forward to, he would never have spent so much time calculating the value of Pi. He would have been baking her a Pie! If Euclid had ever beheld a vision of loveliness like the one I see walking into my anti-math class, he would have forgotten all the geometry of lines and planes, and concentrated on the sweet simplicity of soft curves. If Pythagoras had ever had a girl look at him the way Gloria's eyes fix in my direction, he would have given up his calculations on the hypotenuse of right triangles and run for the hills to pick a bouquet of wildflowers. — David Klass

Being perpetually charmed by his familiar siren, that is, by his geometry, he neglected to eat and drink and took no care of his person; that he was often carried by force to the baths, and when there he would trace geometrical figures in the ashes of the fire, and with his finger draws lines upon his body when it was anointed with oil, being in a state of great ecstasy and divinely possessed by his science. — Plutarch

Everything is roughness, except for the circles. How many circles are there in nature? Very, very few. The straight lines. Very shapes are very, very smooth. But geometry had laid them aside because they were too complicated. — Benoit Mandelbrot

And so will I here state just plainly and briefly that I accept God. But I must point out one thing: if God does exist and really created the world, as we well know, he created it according to the principles of Euclidean geometry and made the human brain capable of grasping only three dimensions of space. Yet there have been and still are mathematicians and philosophers-among them some of the most outstanding-who doubt that the whole universe or, to put it more generally, all existence was created to fit Euclidean geometry; they even dare to conceive that two parallel lines that, according to Euclid, never do meet on earth do, in fact, meet somewhere in infinity. And so my dear boy, I've decided that I am incapable of understanding of even that much, I cannot possibly understand about God. — Fyodor Dostoyevsky

One might suppose that reality must be held to at all costs. However, though that may be the moral thing to do, it is not necessarily the most useful thing to do. The Greeks themselves chose the ideal over the real in their geometry and demonstrated very well that far more could be achieved by consideration of abstract line and form than by a study of the real lines and forms of the world; the greater understanding achieved through abstraction could be applied most usefully to the very reality that was ignored in the process of gaining knowledge. — Isaac Asimov

every day could bring the breaking of a new record, but the larger world would persist undisturbed. There was always news, even if little of it was newsworthy. Every pitch was different, every swing, and yet they all were variations on a familiar theme. The lines on the field, the fences around it, the neat geometry suggested that these, for a discrete but somehow infinite period, were the limits of the world. — Matthew Thomas

His way had therefore come full circle, or rather had taken the form of an ellipse or a spiral, following as ever no straight unbroken line, for the rectilinear belongs only to Geometry and not to Nature and Life. — Hermann Hesse

Straight lines evidently belonged only to geometry, not to nature and life. — Hermann Hesse

Yet there have been and still are mathematicians and philosophers who doubt whether the whole universe, or to speak more widely, the whole of being, was only created in Euclid's geometry. They even dare to dream that two parallel lines, which according to Euclid can never meet on earth, may meet somewhere in infinity. — Fyodor Dostoyevsky

There have been and still are geometricians and philosophers, and even some of the most distinguished, who doubt whether the whole universe, or to speak more widely the whole of existence, was only created in Euclid's geometry; they even dare to dream that two parallel lines, which according to Euclid can never meet on earth, may meet somewhere in infinity. I have come to the conclusion that, since I can't understand even that, I can't expect to understand about God. I acknowledge humbly that I have no faculty for settling such questions, I have a Euclidean earthly mind, and how could I solve problems that are not of this world? And I advise you never to think about it either, my dear Alyosha, especially about God, whether He exists or not. All such questions are utterly inappropriate for a mind created with an idea of only three dimensions. — Fyodor Dostoyevsky

The swirling lines of snow were composed of separate flakes, and each flake was a cluster of separate ice crystals--scientists had counted over a hundred of them in a single flake. Under the microscope each minuscule crystal, colorless and transparent, revealed a secret symmetry: six sides, the outward expression of an inward geometry of frozen molecules of water. But the real wonder was that no two crystals were precisely alike. In one of this father's camera magazines he had seen a stunning display of photomicrographs, and what was most amazing about the enlarged crystals was that each contained in its center a whole world of intricate six-sided designs, caused by microscopic air pockets. For no conceivable reason, Nature in a kind of exuberance created an inexhaustible outpouring of variations on a single form. A snowstorm was a fall of jewels, a delirium of hexagons--clearly the work of a master animator. — Steven Millhauser

We therefore find that the triangles and rectangles herein described, enclose a large majority of the temples and cathedrals of the Greek and Gothic masters, for we have seen that the rectangle of the Egyptian triangle is a perfect generative medium, its ratio of five in width to eight in length 'encouraging impressions of contrast between horizontal and vertical lines' or spaces; and the same practically may be said of the Pythagorean triangle — Samuel Colman

In his ... 'Geometrical peculiarities of the Pyramids', Ballard shows the relationship between the equal area theory and the golden number. After checking Herodotus' statement via dimensions Ballard concludes: 'I have therefore the authority of Herodotus to support the theory which I shall subsequently set forth, that this pyramid was the exponent of lines divided in mean and extreme ratio. — Roger Herz-Fischler

The ship's lines were an elegant array of pure geometry, essentially nothing more than a series of cubes suspended within a curved plane. — Dan Lopez

Fractal geometry is everywhere, even in lines drawn in the sand. It's the cycle of life ... You see fractals in plants, in flowers. Within the human lung are branches within branches. — Ron Eglash

The sharply precise divisions and boundaries, together with the fact that - wind and your more exotic-type spins aside - balls can be made to travel in straight lines only, make textbook tennis plane geometry. It is billiards with balls that won't hold still. It is chess on the run. It is to artillery and airstrikes what football is to infantry and attrition. — David Foster Wallace

Geometry became a symbol for human relations, except that it was better, because in geometry things never go bad. If certain things occur, if certain lines meet, an angle is born. You cannot fail. It's not going to fail; it is eternal. I found in rules of mathematics a peace and a trust that I could not place in human beings. This sublimation was total and remained total. Thus, I'm able to avoid or manipulate or process pain. — Louise Bourgeois

The description of right lines and circles, upon which geometry is founded, belongs to mechanics. Geometry does not teach us to draw these lines, but requires them to be drawn. — Isaac Newton

The world of shapes, lines, curves, and solids is as varied as the world of numbers, and it is only our long-satisfied possession of Euclidean geometry that offers us the impression, or the illusion, that it has, that world, already been encompassed in a manageable intellectual structure. The lineaments of that structure are well known: as in the rest of life, something is given and something is gotten; but the logic behind those lineaments is apt to pass unnoticed, and it is the logic that controls the system. — David Berlinski