Quotes About Geometry

The sine of an angle is the ratio of the lengths of the side of the triangle opposite the angle and the hypotenuse.

The Greek thinkers was no way of bridging the gap between the rectilinear and the curvilinear which would at the same time satisfy their strict demands of mathematical rigor and appeal to the clear evidence of sensory experience.

Recognizing that geometry is entirely intellectual and independent of the actual description and existence of figures, Fontenelle did not discuss the subject fro the point of view of science or metaphysics as had Aristotle and Leibnez.

Most of his predecessors had considered the differential calculus as bound up with geometry, but Euler made the subject a formal theory of functions which had no need to revert to diagrams or geometrical conceptions.

the time will come, and come soon, in which we shall have a knowledge of God and mind that is not less certain than that of figures and numbers, and in which the invention of machines will be no more difficult than the construction of problems in geometry.

Let us now divide the time interval from o to t into a large number of very short time intervals and draw vertical lines as shown in the figure, thus forming a large number of thin tall rectangles.

Repeating the same argument for each thin rectangle, we come to the conclusion that the total distance covered during the time interval (o,t) is equal to the area of the staircase or, in the limit, to the area of the triangle ABC.

We cannot think a line without drawing it in thought; we cannot think a circle without describing it; we cannot represent, at all, the three dimensions of space without placing, from the same point, three lines perpendicularly to one another; we cannot even represent time, except by attending, while drawing a straight line [...]

I made a photograph of a garden in Kyoto, the Zen garden, which is a rectangle. But a photograph taken from any one point will not show, well it shows a rectangle, but not with ninety degree angles.

The beams and bridges cut the light on the ground into little triangles and the rails run round

Plane geometry is sort of the key course where you learn about proving things and abstraction.

One of the great sources of employment for people with Ph.D.s in geometry is the animation industry.

As her lips changed the geometry, Her smile turned to poetry.

Mother Nature did not attend high school geometry courses or read the books of Euclid of Alexandria. Her geometry is jagged, but with a logic of its own and one that is easy to understand.

Or maybe it is only that we are so habitually inattentive that when some rare but simple geometry grabs us by the shoulders and shakes us into consciousness, we call our response sacred.

In other words, the diagonal of that square is irrational—and nowadays we recognize that number as the square root of two.

a mathematician could show how a triangle's angles sum to 180 degrees, or any other geometric fact. On the other hand, calculus was based on faith.

Non-euclidian sofa

The theorem is a hack on discrete number theory that simultaneously disproves the Church-Turing hypothesis (wave if you understood that) and worse, permits NP-complete problems to be converted into P-complete ones. This has several consequences, starting with screwing over most cryptography algorithms—translation: all your bank account are belong to us—and ending with the ability to computationally generate a Dho-Nha geometry curve in real time. This

one point, Leah gave CJ a tough geometry problem in our Berlin hotel room. He collapsed to the floor, where he began crying and saying repeatedly that he wanted to be a taco.

The Greeks, meanwhile, explicitly rejected zero. Since their mathematical system was based on geometry, numbers had to represent space of one sort or another—length, angles, area, etc. Zero space didn't make sense.

I remember, at MIT, we had to write an essay about something mathematical that you do in your extra time. I basically wrote about how dance, to me, was geometry: it was all shapes.

Tequila, scorpion honey, harsh dew of the doglands, essence of Aztec, crema de cacti; tequila, oily and thermal like the sun in solution; tequila, liquid geometry of passion; Tequila, the buzzard god who copulates in midair with the ascending souls of dying virgins; tequila, firebug in the house of good taste; O tequila, savage water of sorcery, what confusion and mischief your sly, rebellious drops do generate!

Squares were good. Efficient. He approved of squares.