Best 92 quotes in «geometry quotes» category

In a way, art is a theory about the way the world looks to human beings. It’s abundantly obvious that one doesn’t know the world around us in detail

In geometry, whenever we had to find the area of a circle, pi * radius squared, I would get really hungry for pie. Square pie.

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.

Is everyone with one face called a Milo?" "Oh no," Milo replied; "some are called Henry or George or Robert or John or lots of other things." "How terribly confusing," he cried. "Everything here is called exactly what it is. The triangles are called triangles, the circles are called circles, and even the same numbers have the same name. Why, can you imagine what would happen if we named all the twos Henry or George or Robert or John or lots of other things? You'd have to say Robert plus John equals four, and if the four's name were Albert, things would be hopeless." "I never thought of it that way," Milo admitted. "Then I suggest you begin at once," admonished the Dodecahedron from his admonishing face, "for here in Digitopolis everything is quite precise.

Is it possible that mathematical pathology, i.e. chaos, is health? And that mathematical health, which is the predictability and differentiability of this kind of a structure, is disease?

It is well known that geometry presupposes not only the concept of space but also the first fundamental notions for constructions in space as given in advance. It only gives nominal definitions for them, while the essential means of determining them appear in the form of axioms. The relationship of these presumptions is left in the dark; one sees neither whether and in how far their connection is necessary, nor a priori whether it is possible. From Euclid to Legendre, to name the most renowned of modern writers on geometry, this darkness has been lifted neither by the mathematicians nor the philosophers who have laboured upon it.

it struck me as an operational way to define free will, in a way that allowed you to reconcile free will with determinism. The system is deterministic, but you can’t say what it’s going to do next.

Mathematics is not just a subject of education system, it is the soul of education system.

In the pentagram, the Pythagoreans found all proportions well-known in antiquity: arithmetic, geometric, harmonic, and also the well-known golden proportion, or the golden ratio. ... Probably owing to the perfect form and the wealth of mathematical forms, the pentagram was chosen by the Pythagoreans as their secret symbol and a symbol of health. - Alexander Voloshinov [As quoted in Stakhov]

Maths is at only one remove from magic.

One simple but powerful consequence of the fractal geometry of surfaces is that surfaces in contact do not touch everywhere. The bumpiness at all scales prevents that. Even in rock under enormous pressure, at some sufficiently small scale it becomes clear that gaps remain, allowing fluid to flow.

Speed is simply the rite that initiates us into emptiness: a nostalgic desire for forms to revert to immobility, concealed beneath the very intensification of their mobility. Akin to the nostalgia for living forms that haunts geometry.

Philosophy is written in this all-encompassing book that is constantly open to our eyes, that is the universe; but it cannot be understood unless one first learns to understand the language and knows the characters in which it is written. It is written in mathematical language, and its characters are triangles, circles, and other geometrical figures; without these it is humanly impossible to understand a word of it, and one wanders in a dark labyrinth.

sacred knowledge of the cosmos seems to be hidden within our souls and is shown within our artwork and creative expressions.

Some of the greatest mathematical minds of all ages, from Pythagoras and Euclid in ancient Greece, through the medieval Italian mathematician Leonardo of Pisa and the Renaissance astronomer Johannes Kepler, to present-day scientific figures such as Oxford physicist Roger Penrose, have spent endless hours over this simple ratio and its properties. But the fascination with the Golden Ratio is not confined just to mathematicians. Biologists, artists, musicians, historians, architects, psychologists, and even mystics have pondered and debated the basis of its ubiquity and appeal. In fact, it is probably fair to say that the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics.

Self-similarity is symmetry across scale. It implies recursion, pattern inside of pattern.

Simple shapes are inhuman. They fail to resonate with the way nature organizes itself or with the way human perception sees the world.

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 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 Ark of the Covenant is a Golden Rectangle because its rectangular shape is in the proportions of the Golden Ratio.

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

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

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

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.

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

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.

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.

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.

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

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.

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

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

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!

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.

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

A pool game mixes ritual with geometry.

Geometry existed before creation.

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

Geometry enlightlens the intellect and sets one's mind right

Geometry is the rules of all mental investigation

Geometry is knowledge of the eternally existent.

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

Geometry is one of the handles of science and philosophy.