Quotes About Geometry

The sacred geometry of chance, sir.

Modern man does not live in space and time, but in geometry and chronometry.

Man today does not live in space and time. But in geometry and chronometers.

The abstract, curvilinear motifs of ancient Islamic decorative art found in mosaics and carpet design appear again and again at all scales of magnification on the boundary of the Mandelbrot set.

Arthur C. Clarke thinks that it may be just a coincidence, "but", he writes, "the Mandelbrot set does indeed seem to contain an enormous number of mandalas or religious symbols, which are found in ecclesiastical designs-such as stained glass windows, and particularly in Islamic art. We find many forms like the Paisley pattern echoing the Mandelbrot set centuries before it was discovered!

The process of rotating, stretching, and moving is called an affine transformation.

Dimensional Magic We are fractal. Our lungs, our circulatory system, our brains are like trees. They are fractal structures. Fractal geometry allows bounded curves of infinite length, and closed surfaces with an infinite area. It even allows curves with positive volume, and arbitrarily large groups of shapes with exactly the same boundary. This is exactly how our lungs manage to maximize their surface area.

The signature of chaos is the fractal attractor-fractals are the patterns of chaos

Psychoanalysis and Zen, in my private psychic geometry, are equal to nicotine. They are anti-existential. Nicotine quarantines one out of existence.

If triangles had a God, He'd have three sides.

No story is a straight line. The geometry of a human life is too imperfect and complex, too distorted by the laughter of time and the bewildering intricacies of fate to admit the straight line into its system of laws.

Treat nature in terms of the cylinder, the sphere, the cone, all in perspective.

In their later years, each (Einstein and Schrödinger) hoped to find a unified field theory that would fill in the gaps of quantum physics and unite the forces of nature. By extending general relativity to include all of the natural forces, such a theory would replace matter with pure geometry - fulfilling the dream of the Pythagoreans, who believed that "all is number".

He (Riemann) showed that there are three main ways space can be curved- positive curvature, negative curvature, and zero curvature. Thes correspond respectively to elliptic, hyperbolic, and Euclidean flat geometries.

Hence, Einstein's equations beautifully connect the stuff of the universe with the shape of the universe.

By introducing non-Euclidean geometry to theoretical physics, Einstein would transform the field in extraordinary ways. The twelve-year-old clutching the geometry book would have no ways of knowing that his very hands would someday rewrite physical laws in a way that made the book obsolete.

Yarn is fundamental, knots are not. Similarly, Hilbert and Mike envisioned a natural order in which the geometry of fields is foremost and twists manifest themselves as particles.

This, dear Phaedrus, is the most important point: no geometry without the word. Without it, figures are accidents, and neither make manifest nor serve the power of the mind.

Geometry exists as an innate phenomenon in our consciousness. In the external world a perfectly formed snow crystal would never exist. But in our consciousness lies the glittering and flawless knowledge of perfect ice.

In the four corners of the outer court there were enclosed courts, each forty cubits long and thirty cubits wide. Each of the four corner areas had the same dimensions.