The full impact of the Lobachevskian method of challenging axioms has probably yet to be felt. It is no exaggeration to call Lobachevsky the Copernicus of Geometry [as did Clifford], for geometry is only a...

I guess a sock is also a geometric shape—technically—but I don’t know what you’d call it. A socktagon?

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...

His way had therefore come full circle, or rather had taken the form of an ellipse or a spiral, following as ever no straight unbroken line, for the rectilinear belongs only to Geometry and not...

Geometry is the language of time.

The best that Gauss has given us was likewise an exclusive production. If he had not created his geometry of surfaces, which served Riemann as a basis, it is scarcely conceivable that anyone else would...

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...

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

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...

The language of time is geometry.

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

You can’t criticize geometry. It’s never wrong.

The early sense of self-similarity as an organizing principle came from the limitations on the human experience of scale.

A circle has no end.

I was very slow in maths, geometry I actually enjoyed.

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...

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?

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...

Philosophy [nature] is written in that great book which ever is before our eyes — I mean the universe — but we cannot understand it if we do not first learn the language and grasp...

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,...

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...

I would say, if you like, that the party is like an out-moded mathematics…that is to say, the mathematics of Euclid. We need to invent a non-Euclidian mathematics with respect to political discipline.

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

[As a young teenager] Galois read Legendre]’s geometry from cover to cover as easily as other boys read a pirate yarn.

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...

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...

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

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

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...

Perfect hexagonal tubes in a packed array. Bees are hard-wired to lay them down, but how does an insect know enough geometry to lay down a precise hexagon? It doesn’t. It’s programmed to chew up...

Of all the possible pathways of disorder, nature favors just a few.

Give me a place to stand, a lever long enough and a fulcrum. and I can move the Earth

IN THE MIND’S EYE, a fractal is a way of seeing infinity.

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...

V geometrickém světě, jehož objev byl umožněn onou pozoruhodnou schopností proniknout skrze čtverec nakreslený v písku ke čtverci geometrickému, nalezla řecká antika místo, v němž se nachází pravda v ničím nezastřené podobě.

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

When there were no customers, he thought about geometry. He tried to perform the Pythagorean Theorem on the light fixture above him, given his estimate of its circumference, but he failed. He wanted to be...

In reality the universe has no geometry.

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....

Be honest: did you actually read [the above geometric proof]? Of course not. Who would want to? The effect of such a production being made over something so simple is to make people doubt their...

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...

Gosta da música, que é a mesma coisa que ouvir geometria

He could not believe that any of them might actually hit somebody. If one did, what a nowhere way to go: killed by accident; slain not as an individual but by sheer statistical probability, by...

… 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...

Geometry has two great treasures; one is the Theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold; the second...

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

As for methods I have sought to give them all the rigour that one requires in geometry, so as never to have recourse to the reasons drawn from the generality of algebra.

It is to geometry that we owe in some sort the source of this discovery [of beryllium]; it is that [science] that furnished the first idea of it, and we may say that without it...

Have you ever wanted to learn Geometry, Calculus, Physics, German, and the mystical teachings of Orafoura? Well, now you can! Just not with this book. Well, except for the mystical bit. This book is guaranteed...

Everybody at the party is a many sided polygon….Nonagon!