Top 365 Geometry Quotes & Sayings

Where there is matter, there is geometry.

I was allergic to school. I was completely befuddled by school. I was trying so hard, but I couldn't succeed. I took geometry for four years, the same course over and over again, and I did not graduate with my senior class. I finally passed geometry after doing summer school, and eventually, I graduated.

A pool at the edge of the ocean is the simplest geometry, yet you feel connected to the sea. In a forest with the mountains in the background, you also feel the connection to nature, yet it's a very complex geometry. I think architecture is about controlling these feelings.

One of the high points of my life was when I suddenly realized that this dream I had in my late adolescence of combining pure mathematics, very pure mathematics with very hard things which had been long a nuisance to scientists and to engineers, that this combination was possible and I put together this new geometry of nature, the fractal geometry of nature.

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

Metrical geometry is thus a part of descriptive geometry, and descriptive geometry is all geometry.

Algebra is nothing more than geometry, in words; geometry is nothing more than algebra, in pictures.

I am coming more and more to the conviction that the necessity of our geometry cannot be demonstrated, at least neither by, nor for, the human intellect. . . Geometry should be ranked, not with arithmetic, which is purely aprioristic, but with mechanics.

Geometry existed before creation.

Poetry is a subject as precise as geometry.

About Thomas Hobbes: He was 40 years old before he looked on geometry; which happened accidentally. Being in a gentleman's library, Euclid's Elements lay open, and "twas the 47 El. libri I" [Pythagoras' Theorem]. He read the proposition "By God", sayd he, "this is impossible:" So he reads the demonstration of it, which referred him back to such a proposition; which proposition he read. That referred him back to another, which he also read. Et sic deinceps, that at last he was demonstratively convinced of that truth. This made him in love with geometry.

Fractions, decimals, algebra, geometry, trigonometry, calculus, mechanics - these are the steps up the mountain side. How high is one going to get? For me, the pinnacle was Projective Geometry. Who today has even heard of this branch of mathematics?

Geometry is the foundation of all painting.

Geometry is one of the handles of science and philosophy.

Let no one destitute of geometry enter my doors.

Projective geometry is all geometry.

Music is geometry in time.

Geometry is knowledge of the eternally existent.

It is through geometry that one purifies the eye of the soul.

. . . by natural selection our mind has adapted itself to the conditions of the external world. It has adopted the geometry most advantageous to the species or, in other words, the most convenient. Geometry is not true, it is advantageous.

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.

Geometry was the first exciting course I remember.

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.

Geometry enlightens the intellect and sets one's mind right. All of its proofs are very clear and orderly. It is hardly possible for errors to enter into geometrical reasoning, because it is well arranged and orderly. Thus, the mind that constantly applies itself to geometry is not likely to fall into error. In this convenient way, the person who knows geometry acquires intelligence.

The description of right lines and circles, upon which geometry is founded, belongs to mechanics. Geometry does not teach us to draw these lines, but requires them to be drawn.

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!

There are no sects in geometry.

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.

Geometry existed before the creation. It is co-eternal with the mind of God...Geometry provided God with a model for the Creation.

Geometry draws the soul towards truth.

A proposition of geometry does not compete with life; and a proposition of geometry is a fair and luminous parallel for a work of art. Both are reasonable, both untrue to the crude fact; both inhere in nature, neither represents it.

Descartes constructed as noble a road of science, from the point at which he found geometry to that to which he carried it, as Newton himself did after him. ... He carried this spirit of geometry and invention into optics, which under him became a completely new art.

Geometry is not true, it is advantageous.

Regular geometry, the geometry of Euclid, is concerned with shapes which are smooth, except perhaps for corners and lines, special lines which are singularities, but some shapes in nature are so complicated that they are equally complicated at the big scale and come closer and closer and they don't become any less complicated.

Pi is not merely the ubiquitous factor in high school geometry problems; it is stitched across the whole tapestry of mathematics, not just geometry's little corner of it. Pi occupies a key place in trigonometry too. It is intimately related to e, and to imaginary numbers. Pi even shows up in the mathematics of probability

A fine image is geometry, modulated by the heart

I love making object form; I wish I was doing more of it. I admire the research of my colleagues, and sometimes it makes me sad when their beautiful work - the deep dives into formal research and nuances of geometry and so on - ends up circling in more and more circumscribed contexts. I wish they were more powerful. It's not a modern proposition. Active form doesn't kill object form. I want my students to have all those skills related to geometry, shape, measure, scale, etc., plus skills for using space to manipulate power in the world.

There is no royal road to geometry.

Sire, there is no royal road to geometry.

Writing is the geometry of the soul.

Geometry is the rules of all mental investigation

A pool game mixes ritual with geometry.

Geometry is the noblest branch of physics.

The purely formal language of geometry describes adequately the reality of space. We might say, in this sense, that geometry is successful magic. I should like to state a converse: is not all magic, to the extent that it is successful, geometry?

In fact, Gentlemen, no geometry without arithmetic, no mechanics without geometry... you cannot count upon success, if your mind is not sufficiently exercised on the forms and demonstrations of geometry, on the theories and calculations of arithmetic ... In a word, the theory of proportions is for industrial teaching, what algebra is for the most elevated mathematical teaching.

I conceived, developed and applied in many areas a new geometry of nature, which finds order in chaotic shapes and processes. It grew without a name until 1975, when I coined a new word to denote it, fractal geometry, from the Latin word for irregular and broken up, fractus. Today you might say that, until fractal geometry became organized, my life had followed a fractal orbit.

Why waste words? Geometry existed before the Creation, is co-eternal with the mind of God, is God himself (what exists in God that is not God himself?): geometry provided God with a model for the Creation and was implanted into man, together with God's own likeness - and not merely conveyed to his mind through the eyes.

Greek architecture is the flowering of geometry.

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

One geometry cannot be more true than another; it can only be more convenient. Geometry is not true, it is advantageous.

Logic was to cognition as geometry was to landscape

Gravity is a response to geometry.

... geometry became a symbol for human relations, except that it was better, because in geometry things never go bad. If certain things occur, if certain lines meet, an angle is born. You cannot fail. It's not going to fail; it is eternal. I found in rules of mathematics a peace and a trust that I could not place in human beings. This sublimation was total and remained total. Thus, I'm able to avoid or manipulate or process pain.

Every field has its taboos. In algebraic geometry the taboos are (1) writing a draft that can be followed by anyone but two or three of one's closest friends, (2) claiming that a result has applications, (3) mentioning the word 'combinatorial,' and (4) claiming that algebraic geometry existed before Grothendieck (only some handwaving references to 'the Italians' are allowed provided they are not supported by specific references).

Geometry is the archetype of the beauty of the world.

The concept of congruence in Euclidean geometry is not exactly the same as that in non-Euclidean geometry. ..."Congruent" means in Euclidean geometry the same as "determining parallelism," a meaning which it does not have in non-Euclidean geometry.

Geometry, like arithmetic, requires for its logical development only a small number of simple, fundamental principles. These fundamental principles are called the axioms of geometry.

Poetry is as precise a thing as geometry.

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 have discovered it. I do not hesitate to confess that to a certain extent a similar pleasure may be found by absorbing ourselves in questions of pure geometry.

Geometry is the most complete science.