There is geometry in the humming of the strings, there is music in the spacing of the spheres.

— Pythagoras

### Algebra is nothing more than geometry, in words;

geometry is nothing more than algebra, in pictures.

### Where there is matter, there is geometry.

Fractal geometry is not just a chapter of mathematics, but one that helps Everyman to see the same world differently.

### Geometry is the archetype of the beauty of the world.

A geometry implies the heterogeneity of locus, namely that there is a locus of the Other. Regarding this locus of the Other, of one sex as Other, as absolute Other, what does the most recent development in topology allow us to posit?

Architects should be educated, skillful with the pencil, instructed in geometry, know much history, have followed the philosophers with attention, understand music, have some knowledge of medicine, know the opinions of the jurists, and be acquainted with astronomy and the theory of the heavens

### Without mathematics, there’s nothing you can do.

Everything around you is mathematics. Everything around you is numbers.

In right-angled triangles the square on the side subtending the right angle is equal to the squares on the sides containing the right angle.

Why is geometry often described as cold and dry? One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline or a tree.

As long as algebra and geometry have been separated, their progress have been slow and their uses limited; but when these two sciences have been united, they have lent each mutual forces, and have marched together towards perfection.

I conceived and developed a new geometry of nature and implemented its use in a number of diverse fields. It describes many of the irregular and fragmented patterns around us, and leads to full-fledged theories, by identifying a family of shapes I call fractals.

### The mathematical sciences particularly exhibit order symmetry and limitations;

and these are the greatest forms of the beautiful.

Give him threepence, since he must make a gain out of what he learns.

That, if a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which the angles are less than two right angles.

My origami creations, in accordance with the laws of nature, require the use of geometry, science, and physics. They also encompass religion, philosophy, and biochemistry. Overall, I want you to discover the joy of creation by your own handthe possibility of creation from paper is infinite.

Algebra is but written geometry and geometry is but figured algebra.

The composer opens the cage door for arithmetic, the draftsman gives geometry its freedom.

### God looks not at the oratory of your prayers, how elegant they may be;

nor at the geometry of your prayers, how long they may be; nor at the arithmetic of your prayers, how many they may be; not at logic of your prayers, how methodical they may be; but the sincerity of them he looks at.

Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.

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 part of the vaster domain which he renovated; it might even be just to designate him as a Copernicus of all thought.

Music is the arithmetic of sounds as optics is the geometry of light.

I think the universe is pure geometry - basically, a beautiful shape twisting around and dancing over space-time.

I did not know then that this is what life is - just when you master the geometry of one world, it slips away, and suddenly again, you're swarmed by strange shapes and impossible angles.

### Inspiration is needed in geometry, just as much as in poetry.

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.

### Mighty is geometry; joined with art, resistless.

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 we may name a precious jewel.

### Crystals grew inside rock like arithmetic flowers.

They lengthened and spread, added plane to plane in an awed and perfect obedience to an absolute geometry that even stones - maybe only the stones - understood.

### I am present at the sowing of the seed of the world.

With a geometry of sunbeams, the soul lays the foundations of nature.

The sculptor, and the painter also, should be trained in these liberal arts: grammar, geometry, philosophy, medicine, astronomy, perspective, history, anatomy, theory of design, arithmetic.

### A firm rule must be imposed upon our nation before it destroys itself.

The United States needs some theology and geometry, some taste and decency. I suspect that we are teetering on the edge of the abyss.