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Geometry Quotes

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Geometry Quotes

“We admit, in geometry, not only infinite magnitudes, that is to say, magnitudes greater than any assignable magnitude, but infinite magnitudes infinitely greater, the one than the other. This astonishes our dimension of brains, which is only about six inches long, five broad, and six in depth, in the largest heads.”

“I claim that many patterns of Nature are so irregular and fragmented, that, compared with Euclid - a term used in this work to denote all of standard geometry - Nature exhibits not simply a higher degree but an altogether different level of complexity ... The existence of these patterns challenges us to study these forms that Euclid leaves aside as being "formless," to investigate the morphology of the "amorphous."”

“When I began my physical studies [in Munich in 1874] and sought advice from my venerable teacher Philipp von Jolly...he portrayed to me physics as a highly developed, almost fully matured science...Possibly in one or another nook there would perhaps be a dust particle or a small bubble to be examined and classified, but the system as a whole stood there fairly secured, and theoretical physics approached visibly that degree of perfection which, for example, geometry has had already for centuries.”

“When we teach a child to sing or play the flute, we teach her how to listen. When we teach her to draw, we teach her to see. When we teach a child to dance, we teach him about his body and about space, and when he acts on a stage, he learns about character and motivation. When we teach a child design, we reveal the geometry of the world. When we teach children about the folk and traditional arts and the great masterpieces of the world, we teach them to celebrate their roots and find their own place in history.”

“Gregorian chant, Romanesque architecture, the Iliad , the invention of geometry were not, for the people through whom they were brought into being and made available to us, occasions for the manifestation of personality.”

“The classical theorists resemble Euclidean geometers in a non-Euclidean world who, discovering that in experience straight lines apparently parallel often meet, rebuke the lines for not keeping straight as the only remedy for the unfortunate collisions which are occurring. Yet, in truth, there is no remedy except to throw over the axiom of parallels and to work out a non-Euclidean geometry.”

“There is (gentle reader) nothing (the works of God only set apart) which so much beautifies and adorns the soul and mind of man as does knowledge of the good arts and sciences . Many arts there are which beautify the mind of man; but of all none do more garnish and beautify it than those arts which are called mathematical , unto the knowledge of which no man can attain, without perfect knowledge and instruction of the principles, grounds, and Elements of Geometry.”

“Abstraction didn't have to be limited to a kind of rectilinear geometry or even a simple curve geometry. It could have a geometry that had a narrative impact. In other words, you could tell a story with the shapes. It wouldn't be a literal story, but the shapes and the interaction of the shapes and colors would give you a narrative sense. You could have a sense of an abstract piece flowing along and being part of an action or activity. That sort of turned me on.”

“Whatever efforts one may make, one must revert to the realization that religion is the real basis of morality; religion is the real and perceptible purpose within us, which alone, can turn aside our attention from things. ... The science of morality can no more teach human beings to be honest, in all the magnificence of this word, than geometry can teach one how to draw.”

“And in between the two, in between the sky and the sea, were all the winds. And there were all the nights and all the moons. To be a castaway is to be a point perpetually at the centre of a circle. However much things may appear to change-the sea may shift from whisper to rage, the sky might go from fresh blue to blinding white to darkest black-the geometry never changes. Your gaze is always a radius. The circumference is ever great. In fact, the circles multiply. To be a castaway is to be caught in a harrowing ballet of circles.”

“Mathematical demonstrations being built upon the impregnable Foundations of Geometry and Arithmetick are the only truths that can sink into the Mind of Man, void of all Uncertainty; and all other Discourses participate more or less of Truth according as their Subjects are more or less capable of Mathematical Demonstration.”

“The science of the church is neglected for the study of geometry, and they lose sight of Heaven while they are employed in measuring the earth. Euclid is perpetually in their hands. Aristotle and Theophrastus are the objects of their admiration; and they express an uncommon reverence for the works of Galen. Their errors are derived from the abuse of the arts and sciences of the infidels, and they corrupt the simplicity of the gospel by the refinements of human reason.”