Quotes About Geometry

An exquisitely complex shape now known as the Mandlebrot set has been called the most complex object in mathematics.

Now suddenly he had intimations of destiny; he could see that life had a secret geometry on which his rational mind had no purchase. But even as he was overcome with a desire to subdue his reason and find happiness, he also sensed that - for the moment at least - his yearning for happiness was not yet strong enough.

With the sentiment of the stars and moon such nights I get all the free margins and indefiniteness of music or poetry, fused in geometry's utmost exactness.

He turned out to be good in geometry, but he never mastered the use of equations or the rudimentary algebra that existed at the time.

But by 1912, Einstein had come to appreciate that math could be a tool for discovering—and not merely describing—nature's laws. Math was nature's playbook. "The central idea of general relativity is that gravity arises from the curvature of spacetime," says physicist James Hartle. "Gravity is geometry.

Our model of the cosmos must be as inexhaustible as the cosmos. A complexity that includes not only duration but creation, not only being but becoming, not only geometry but ethics. It is not the answer we are after, but only how to ask the question.

The loop approach to quantum gravity is now a thriving field of research. Many of the older ideas, such as supergravity and the study of quantum black holes, have been incorporated into it. Connections have been discovered to other approaches to quantum gravity, such as Alain Connes's non-commutative approach to geometry, Roger Penrose's twistor theory and string theory.

The key question for a quantum theory of gravity is then the following: Can we extend to quantum theory the principle that space has no fixed geometry? That is, can we make quantum theory background-independent, at least with regard to the geometry of space? If we can do this, we will automatically merge gravity and quantum theory, because gravity is already understood to be an aspect of dynamical spacetime geometry.

Thus, the double unification given by the equivalence principle becomes a triple unification: All motions are equivalent once the effects of gravity are taken into account, gravity is indistinguishable from acceleration, and the gravitational field is unified with the geometry of space and time. When worked out in detail, this became Einstein's general theory of relativity, which he published in full form in 1915.

I use geometric and mathematical ideas to organize material, but those are tools. The purpose of the work is not to expose that at all, but to arrive at some kind of expressiveness.

I'd been doing projects outdoors for the public. I made pigeons eat geometry by putting bread out in rhomboids and triangles. I don't know if this activity made sense, but the work was available.

Pool, it became clear to me, is all about angles. First, there are simple angles, as you must hit the cue ball to either side when you are not straight on.

a continuous curve that goes from the lower half-plane to the upper half-plane must cross the horizontal axis at some point.

If I died, would it get me out of my geometry test tomorrow? One could only hope. - Zoey Mongomery (Redbird)

PHI is one H of a lot cooler than PI!

The English philosopher and geometer, Keith Critchlow, brings his own light to the same point: "The human mind takes apart with its analytic habits of reasoning but the human heart puts things together because it loves them . . ."18

It is not merely probable, it is certain that we shall never find a straight line that is not the shortest distance between two points.

Something to forgive is a purer joy than geometry.

Rigid geometry forced in varied curves is "mother," / is "nature," is systematic violation." Muy Bueno. / This device is for you, the mutilated of no art.

I watch the cranes scratching their beaks with their toes and think of how the starling flocks that pour into reed beds like grain turn all of a sudden into birds perching on bowed stems, bright-eyed, their feathers spangled with white spots that glow like small stars. I marvel at how confusion can be resolved by focusing on the things from which it is made. The magic of the flocks is this simple switch between geometry and family.

It is impossible to consider the mechanism of our intellect and the progress of our science without arriving at the conclusion that between intellect and matter there is, in fact, symmetry, concord and agreement. On one hand, matter resolves itself more and more, in the eyes of the scholar, into mathematical relations, and on the other hand, the essential faculties of our intellect function with an absolute precision only when they are applied to geometry.

For me the camera is a sketch book, an instrument of intuition and spontaneity, the master of the instant which, in visual terms, questions and decides simultaneously. In order to "give a meaning" to the world, one has to feel oneself involved in what one frames through the viewfinder. This attitude requires concentration, a discipline of the mind, sensitivity, and a sense of geometry.

We often say that the earth is a sphere, but to be precise, the term sphere refers only to the surface. The correct mathematical term for the solid earth is a ball.

Mathematicians didn't invent infinity until 1877. So they thought it was impossible that Africans could be using fractal geometry.