Best 93 of Geometry quotes - MyQuotes
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.
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
Geometry is the rules of all mental investigation
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.
Logic was to cognition as geometry was to landscape
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.
Geometry is not true, it is advantageous.
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
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.
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.
By degrees, the bitterness at my heart diffused itself to the circumference of the circle in which my life went its cheerless mechanical round.
Poetry is a subject as precise as geometry.
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.
Erri De Luca
The geometry of the things around us creates coincidences, intersections.
Self-similarity is symmetry across scale. It implies recursion, pattern inside of pattern.
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.
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.
Poetry is as precise a thing as geometry.
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.
The shortest distance between two points is a straight line. This maxim holds not only in geometry, but in business as well.
In geometric and physical applications, it always turns out that a quantity is characterized not only by its tensor order, but also by symmetry.
Geometry is the art of correct reasoning from incorrectly drawn figures.
Everybody at the party is a many sided polygon....Nonagon!
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.
You don’t see something until you have the right metaphor to let you perceive it
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!
Projective geometry is all geometry.
A circle has no end.
Nicholas Murray Butler
The analytical geometry of Descartes and the calculus of Newton and Leibniz have expanded into the marvelous mathematical method—more daring than anything that the history of philosophy records—of Lobachevsky and Riemann, Gauss and Sylvester. Indeed, mathematics, the indispensable tool of the sciences, defying the senses to follow its splendid flights, is demonstrating today, as it never has been demonstrated before, the supremacy of the pure reason.
John Edensor Littlewood
The first test of potential in mathematics is whether you can get anything out of geometry.
What music is to the heart, mathematics is to the mind.
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 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.
Geometry is the noblest branch of physics.
Simple shapes are inhuman. They fail to resonate with the way nature organizes itself or with the way human perception sees the world.
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]
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.
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.
As to the need of improvement there can be no question whilst the reign of Euclid continues. My own idea of a useful course is to begin with arithmetic, and then not Euclid but algebra. Next, not Euclid, but practical geometry, solid as well as plane; not demonstration, but to make acquaintance. Then not Euclid, but elementary vectors, conjoined with algebra, and applied to geometry. Addition first; then the scalar product. Elementary calculus should go on simultaneously, and come into vector algebraic geometry after a bit. Euclid might be an extra course for learned men, like Homer...
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.
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.
There are infinitely many variations of the initial situation and therefore no doubt indefinitely many theorems of moral geometry.
Geometry is one and eternal shining in the mind of God
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.
Eric Temple Bell
The only royal road to elementary geometry is ingenuity.
... 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.
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.
In geometry, whenever we had to find the area of a circle, pi * radius squared, I would get really hungry for pie. Square pie.
The Creator, the fountain of all wisdom, the approver of perpetual order, the eternal and superessential spring of geometry and harmonics.