Best 92 quotes in «geometry quotes» category

The boundary is where points are slowest to escape the pull of the set. It is as if they are balanced between competing attractors, one at zero and the other, in effect, ringing the set at a distance of infinity.

the brain does not own any direct copies of stuff in the world. There is no library of forms and ideas against which to compare the images of perception. Information is stored in a plastic way, allowing fantastic juxtapositions and leaps of imagination. Some chaos exists out there, and the brain seems to have more flexibility than classical physics in finding the order in it.

The diameter divides into the circumference, you know. It ought to be three times. You'd think so, wouldn't you? But does it? No. Three point one four one and lots of other figures. There's no end to the buggers. Do you know how pissed off that makes me?" "I expect it makes you extremely pissed off," said Teppic politely. "Right. It tells me that the Creator used the wrong kind of circles. It's not even a proper number! I mean, three point five, you could respect. Or three point three. That'd look *right*." He stared morosely at the pie.

The fractal structure nature has devised works so efficiently that, in most tissue, no cell is ever more than three or four cells away from a blood vessel. Yet the vessels and blood take up little space, no more than about five percent of the body.

The geometry of the things around us creates coincidences, intersections.

The geometry of sky extends its angles. Look, beyond the hemisphere of pen and book. Technicians by Jean Kenward

The Golden Ratio defines the squaring of a circle. Stated in mathematical terms, this says: Given a square of known perimeter, create a circle of equal circumference. According to some, in ancient Egypt, this mathematical mystery was encoded in the measurements of the Great Pyramid of Giza.

[The golden proportion] is a scale of proportions which makes the bad difficult [to produce] and the good easy.

The Greeks made Space the subject-matter of a science of supreme simplicity and certainty. Out of it grew, in the mind of classical antiquity, the idea of pure science. Geometry became one of the most powerful expressions of that sovereignty of the intellect that inspired the thought of those times. At a later epoch, when the intellectual despotism of the Church, which had been maintained through the Middle Ages, had crumbled, and a wave of scepticism threatened to sweep away all that had seemed most fixed, those who believed in Truth clung to Geometry as to a rock, and it was the highest ideal of every scientist to carry on his science 'more geometrico.

The little Hexagon meditated on this a while and then said to me; "But you have been teaching me to raise numbers to the third power: I suppose three-to-the-third must mean something in Geometry; what does it mean?" "Nothing at all," replied I, "not at least in Geometry; for Geometry has only Two Dimensions." And then I began to shew the boy how a Point by moving through a length of three inches makes a Line of three inches, which may be represented by three; and how a Line of three inches, moving parallel to itself through a length of three inches, makes a Square of three inches every way, which may be represented by three-to-the-second. xxx Upon this, my Grandson, again returning to his former suggestion, took me up rather suddenly and exclaimed, "Well, then, if a Point by moving three inches, makes a Line of three inches represented by three; and if a straight Line of three inches, moving parallel to itself, makes a Square of three inches every way, represented by three-to-the-second; it must be that a Square of three inches every way, moving somehow parallel to itself (but I don't see how) must make Something else (but I don't see what) of three inches every way—and this must be represented by three-to-the-third." "Go to bed," said I, a little ruffled by this interruption: "if you would talk less nonsense, you would remember more sense.

The only things that can ever be universal, in a sense, are scaling things.

The pits and tangles are more than blemishes distorting the classic shapes of Euclidian geometry. They are often the keys to the essence of a thing

the pattern appears so ethereally, that it is hard to remember that the shape is an attractor. It is not just any trajectory of a dynamical system. It is the trajectory toward which all other trajectories converge.

They asked for Plato's assistance. He told them: "You hated wisdom and ran away from geometry, therefore God has afflicted you a punishment, for wisdom and philosophical knowledge have a high rank with God." ... The plague was lifted and they ceased to defame the branches of theoretical knowledge.

The shortest distance between two points is a straight line. This maxim holds not only in geometry, but in business as well.

We shall understand the mode of purification by confession, and that of contemplation by analysis, advancing by analysis to the first notion, beginning with the properties underlying it; abstracting from the body its physical properties, taking away the dimension of depth, then that of breadth, and then that of length. For the point which remains is a unit, so to speak, having position; from which if we abstract position, there is the conception of unity.

They say the silence is the language of God, but so is music. This is why we dance, we become loud in our silence.

This relationship, often called the Golden mean, has been discovered and rediscovered at various times in history as a unique proportion believed to have both aesthetic and mystic significance. That the Egyptians knew of it and used it seems certain.

To a scholar, mathematics is music.

What if Loves are analogous to math? First, arithmetic, then geometry and algebra, then trig and quadratics…

A pool game mixes ritual with geometry.

Analytical geometry has never existed. There are only people who do linear geometry badly, by taking coordinates, and they call this analytical geometry. Out with them!

What music is to the heart, mathematics is to the mind.

You don’t see something until you have the right metaphor to let you perceive it

An American is a complex of occasions, themselves a geometry of spatial nature.

Books, Manuals, Directives, Regulations. The geometries that circumscribe your working life draw norrower and norrower until nothing fits inside them anymore.

Geometry existed before creation.

Geometry enlightlens the intellect and sets one's mind right

Geometry is the only science that it hath pleased God hitherto to bestow on mankind.

Geometry is the rules of all mental investigation

Geometry is knowledge of the eternally existent.

Geometry is one of the handles of science and philosophy.

Geometry is the science of correct reasoning on incorrect figures.

Geometry is not true, it is advantageous.

Geometry is one and eternal shining in the mind of God

Geometry is the art of correct reasoning from incorrectly drawn figures.

Geometry is the noblest branch of physics.

Gravity is a response to geometry.

It [ non-Euclidean geometry ] would be ranked among the most famous achievements of the entire [nineteenth] century, but up to 1860 the interest was rather slight.

Greek architecture is the flowering of geometry.

In geometric and physical applications, it always turns out that a quantity is characterized not only by its tensor order, but also by symmetry.

How many theorems in geometry which have seemed at first impracticable are in time successfully worked out!

Logic was to cognition as geometry was to landscape

It turns out that hyperbolic structures are very common in nature, and the place where lots of people encounter them is coral reefs. Sea slugs, and a lot of other organisms with frilly forms, are biological manifestations of hyperbolic geometry, which is also found in the structure of lettuce leaves and kales, and some species of cactus.

Life is merely a fracas on an unmapped terrain, and the universe a geometry stricken with epilepsy.

Now, a 45-degree angle is not something we deal with in finance. It's something you see in a high school geometry class. Performance like that has never been recorded in human history.

Not that the propositions of geometry are only approximately true, but that they remain absolutely true in regard to that Euclidean space which has been so long regarded as being the physical space of our experience.

One geometry cannot be more true than another; it can only be more convenient.

There are infinitely many variations of the initial situation and therefore no doubt indefinitely many theorems of moral geometry.

Poetry is a subject as precise as geometry.