Geometric concepts Quotes

Symmetrical equations are good in their place, but ' vector ' is a useless survival, or offshoot from quaternions, and has never been of the slightest use to any creature.

The best that Gauss has given us was likewise an exclusive production. If he had not created his geometry of surfaces, which served Riemann as a basis, it is scarcely conceivable that anyone else would have discovered it. I do not hesitate to confess that to a certain extent a similar pleasure may be found by absorbing ourselves in questions of pure geometry.

I do not want to presuppose anything as known. I see in my explanation in section 1 the definition of the concepts point, straight line and plane, if one adds to these all the axioms of groups i-v as characteristics. If one is looking for other definitions of point, perhaps by means of paraphrase in terms of extensionless, etc., then, of course, I would most decidedly have to oppose such an enterprise. One is then looking for something that can never be found, for there is nothing there, and everything gets lost, becomes confused and vague, and degenerates into a game of hide and seek.

Geometry in every proposition speaks a language which experience never dares to utter; and indeed of which she but halfway comprehends the meaning.

In the meantime, most noble Sir, you have assigned this question to the geometry of position, but I am ignorant as to what this new discipline involves, and as to which types of problem Leibniz and Wolff expected to see expressed in this way.

The fools think I am writing algebra but what I am really writing is geometry.

Equations are just the boring part of mathematics. I attempt to see things in terms of geometry.

The straightest line between a straight distance is two points.

Hippocrates is an excellent geometer but a complete fool in everyday affairs.

Thanks to the oval I have discovered the meaning of the horizontal and the vertical.

The line has magnitude in one way, the plane in two ways, and the solid in three ways, and beyond these there is no other magnitude because the three are all.

An oblique angle,” Jack said, and his bout of jealousy was quickly replaced with glee. “Ha! I told you I would work that in!

Bodies are real entities. Surfaces and lines are but fictitious entities. A surface without depth, a line without thickness, was never seen by any man; no; nor can any conception be seriously formed of its existence.

I have an infamously low capacity for visualizing relationships, which made the study of geometry and all subjects derived from it impossible for me.

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.

I regret that it has been necessary for me in this lecture to administer a large dose of four-dimensional geometry. I do not apologize, because I am really not responsible for the fact that nature in its most fundamental aspect is four-dimensional. Things are what they are.

The straight line is regarded as the shortest distance between two people, as if they were points.

I think my mom gave me the borders, the - gave me a very clear understanding of what the perimeter was. And I had to find my fun within those boundaries.

Number, place, and combination . . . the three intersecting but distinct spheres of thought to which all mathematical ideas admit of being referred.

To grasp the essence of chirality, it is instructive to withdraw for a moment from the familiar three-dimensional world into a two-dimensional one, into a plane, and enquire what chirality means there.