Whoever thinks algebra is a trick in obtaining unknowns has thought it in vain. No attention should be paid to the fact that algebra and **geometry** are different in appearance. Algebras (jabbre and maqabeleh) are geometric facts which are proved by propositions five and six of Book two of Elements.

— As quoted in "A Paper of Omar Khayyam" by A.R. Amir-Moez in

I need **geometry** to set the grammar of the image expressive language . The structural skeleton, the composition and the geometric layout provide a perspective from which one can read the image; otherwise we would do what Dadaists did when they put words in a little bag and then took them out at random in order to compose a poem.

— As quoted in: interview by Flavia Squarcio for

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

— As quoted in

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."

— As quoted in a review of

The doctrine of ratios and proportion is introduced by Euclid as a part of his system of **geometry** ; and the student seldom fails to remark, that in the treatises on algebra, the same subject is presented under a considerably different form; though he is usually quite unable to determine wherein the essential difference consists; and would probably find but few teachers who could precisely point out the distinction to him.

— Rev. Baden Powell,

Visual forms are not perceived differently from colors or brightness. They are sense qualities, and the visual character of **geometry** consists in these sense qualities.

—

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**.

— ?"The Mathematical Preface" to Henry Billingsley's English translation of Euclid's

It is noteworthy that modern Platonists , almost without exception, are ignorant of mathematics, in spite of the immense importance that Plato attached to arithmetic and **geometry**, and the immense influence that they [these studies] had on his philosophy. This is an example of the evils of specialization: a man must not write on Plato unless he has spent so much of his youth on Greek as to have no time for the things that Plato thought important.

— Book One, Part II, Chapter XV, The Theory of Ideas, p. 132

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.

— p. 400 (The Rainbow of Mathematics: A History of the Mathematical Sciences (2000))

Music is **geometry** in time.

—

There are infinitely many variations of the initial situation and therefore no doubt indefinitely many theorems of moral **geometry**.

— Chapter III, Section 21, pg. 126

The progression of a painter’s work, as it travels in time from point to point, will be toward clarity: toward the elimination of all obstacles between the painter and the idea, and between the idea and the observer. As examples of such obstacles, I give (among others) memory, history or **geometry**, which are swamps of generalization from which one might pull out parodies of ideas (which are ghosts) but never an idea in itself. To achieve this clarity is, inevitably, to be understood.

—

In **geometry** his greatest achievement was an accurate value of ?. His rule is stated as: dn^2+(2a-d)n=2s, which implies the approximation 3.1416 which is correct to the last decimal place.

— In, p.245 (Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures)

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.

— Benoît Mandelbrot As quoted in

Anaximander relies on the accuracy of **geometry** in matters beyond the range of any kind of verification in its application to cosmic proportions and also in contradiction to appearance, which suggests that the sun is about as large in diameter as the width of a human foot. The concept of geometrical similarity is also the precondition for Anaximander's attempt to construct a map of the world.

— Walter Burkert,

It is a remarkable fact in the history of **geometry** , that the Elements of Euclid, written two thousand years ago, are still regarded by many as the best introduction to the mathematical sciences.

— Florian Cajori,