Best 93 of Geometry quotes - MyQuotes
Everything is fields, and a particle is just a smaller version of a field. There is a harmonic relationship involved. Disturbing ideas like those of Einstein in 1905 and Feynman Pocono Conference in 1948. Here we go; 1) The universe is ringing like a bell. Neil Turok's Public Lecture: The Astonishing Simplicity of Everything. 2) The stuff of the universe is waves or fields. 3) Scale is relative, not fixed because all of these waves are ratios of one another. 4) The geometry is fractal. This could be physical or computational. 5) If the geometry is computational then, there is no point in speaking about the relationship of the pixels on the display.
Self-similarity is symmetry across scale. It implies recursion, pattern inside of pattern.
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.
What if Loves are analogous to math? First, arithmetic, then geometry and algebra, then trig and quadratics…
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.
There are infinitely many variations of the initial situation and therefore no doubt indefinitely many theorems of moral geometry.
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.
Geometry is the rules of all mental investigation
Geometry existed before creation.
The shortest distance between two points is a straight line. This maxim holds not only in geometry, but in business as well.
[The golden proportion] is a scale of proportions which makes the bad difficult [to produce] and the good easy.
Geometry is one and eternal shining in the mind of God
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.
An American is a complex of occasions, themselves a geometry of spatial nature.
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.
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.
But who can quantify the algebra of space, or weigh those worlds that swim each in its place? Who can outdo the dark? And what computer knows how beauty comes to birth - shell star and rose? -Technicians by Jean Kenward
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.
Charles Sanders Peirce
Kepler’s discovery would not have been possible without the doctrine of conics. Now contemporaries of Kepler—such penetrating minds as Descartes and Pascal—were abandoning the study of geometry ... because they said it was so UTTERLY USELESS. There was the future of the human race almost trembling in the balance; for had not the geometry of conic sections already been worked out in large measure, and had their opinion that only sciences apparently useful ought to be pursued, the nineteenth century would have had none of those characters which distinguish it from the ancien régime.
Simple shapes are inhuman. They fail to resonate with the way nature organizes itself or with the way human perception sees the world.
Mathematics is not just a subject of education system, it is the soul of education system.
To a scholar, mathematics is music.
Poetry is a subject as precise as geometry.
A pool game mixes ritual with geometry.
The detailed geometry of the coenzyme molecule as a whole is fascinating in its complexity.
What physics tells us is that everything comes down to geometry and the interactions of elementary particles. And things can happen only if these interactions are perfectly balanced.
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.
There are no sects in geometry.
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.
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.
Geometry enlightlens the intellect and sets one's mind right
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!
Billions of years ago there were just blobs of protoplasm; now billions of years later here we are. So information has been created and stored in our structure. In the development of one person’s mind from childhood, information is clearly not just accumulated but also generated—created from connections that were not there before
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 Creator, the fountain of all wisdom, the approver of perpetual order, the eternal and superessential spring of geometry and harmonics.
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?
William Kingdon Clifford
Euclid's Elements has been for nearly twenty-two centuries the encouragement and guide of that scientific thought which is one thing with the progress of man from a worse to a better state. The encouragement; for it contained a body of knowledge that was really known and could be relied on, and that moreover was growing in extent and application. For even at the time this book was written—shortly after the foundation of the Alexandrian Museum—Mathematics was no longer the merely ideal science of the Platonic school, but had started on her career of conquest over the whole world of Phenomena. The guide; for the aim of every scientific student of every subject was to bring his knowledge of that subject into a form as perfect as that which geometry had attained. Far up on the great mountain of Truth, which all the sciences hope to scale, the foremost of that sacred sisterhood was seen, beckoning for the rest to follow her.
Geometry is one of the handles of science and philosophy.
Geometry is the only science that it hath pleased God hitherto to bestow on mankind.
A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser.
I forget if it was the Mathematician of Alexandria who said that geometry is beauty laid bare or the Father of Relativity who made the claim for physics,” Darger said. “She is, in either case, ravishing.
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.
Poetry is as precise a thing as geometry.
By degrees, the bitterness at my heart diffused itself to the circumference of the circle in which my life went its cheerless mechanical round.
Books, Manuals, Directives, Regulations. The geometries that circumscribe your working life draw norrower and norrower until nothing fits inside them anymore.
Ralph Waldo Emerson
Greek architecture is the flowering of geometry.
sacred knowledge of the cosmos seems to be hidden within our souls and is shown within our artwork and creative expressions.
Logic was to cognition as geometry was to landscape
... I left Caen, where I was living, to go on a geological excursion under the auspices of the School of Mines. The incidents of the travel made me forget my mathematical work. Having reached Coutances, we entered an omnibus to go to some place or other. At the moment when I put my foot on the step, the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with those of non-Euclidean geometry. I did not verify the idea; I should not have had time, as upon taking my seat in the omnibus, I went on with a conversation already commenced, but I felt a perfect certainty. On my return to Caen, for convenience sake, I verified the result at my leisure.
Geometry is not true, it is advantageous.