Quotes About Geometry

Benoit Mandelbrot can be considered the Euclid of fractal geometry. He has collected the observations of mathematicians concerned with monsters, or objects not definable by euclidean geometry. By combining the work of these mathematicians with his own insight, he has created a geometry of nature that thrives on asymmetry and roughness. Mandelbrot has said that mountains are not cones, and clouds are not spheres.

Once, I went to the roof of a project and saw a hawk perched on the rail; always, you see the city in the near distance, its towers and spires studded with lights, both stately and slapdash, like the crazy geometry of rock crystal. There were many days when you felt sorry for people who worked inside.

The geometry! I think I can see it! Each quarter section is homeomorphic to a triangle!

George Washington, the first president of the United States, mastered geometry, trigonometry, and surveying at about the age of twelve, though folks in his day did not consider him particularly bright.

When I do the dodecahedron with the science audiences, I'll point out that I can only do three of the five forms with bubbles, since bubbles only join at three-way corners. The two I can't do are the ones that represent water and air. That always gets a big laugh from the mathematicians. They see the irony in it.

The waves from all the different parts of a sphere would cancel each other out. You need motion that's nonspherical.

Planets' orbits are elliptical. It's a very pleasing shape.

Los orígenes del método están, según nos cuenta Descartes ( Discurso), en la lógica, el análisis geométrico y el álgebra. Conviene ante todo insistir en que el gravísimo defecto de la lógica de Aristóteles es, para Descartes, su incapacidad de invención.

The Golden Mean was considered a fundamental constant by the Egyptians and the fundamental division of the whole into two parts.

Rachel bit her lip. I hope you're right. I'm a little worried. What if someone asks what's on the next math test and I start spouting a prophecy in the middle of geometry class? The Pythagorean theorem shall be problem two... Gods, that would be embarrassing.

Arithmetic and number theory study patterns of number and counting. Geometry studies patterns of shape. Calculus allows us to handle patterns of motion. Logic studies patterns of reasoning. Probability theory deals with patterns of chance. Topology studies patterns of closeness ans position.

The number system we use today—the Hindu-Arabic system—was developed in India and seems to have been completed by around 700 CE. Indian mathematicians made advances in what would today be described as arithmetic, algebra, and geometry, much of their work being motivated by an interest in astronomy. The system is based on three key ideas: notations for the numerals, place value, and zero.

My stepfather, the builder, taught me how to perform certain operations in geometry: how to divide a line exactly in half, how to draw a right angle, and how to draw one square inside another so that the smaller is half the area of the larger.

But who shall parcel out His intellect by geometric rules, Split like a province into round and square?

I ran into Isosceles. He had a great idea for a new triangle!

A real line has only one dimension, and that means it is impossible to draw it on a piece of real paper.

I dearly wished the joy of triangulation, the pounce based on a good ear's geometry.

It appears then that the essence of chess is its abstract structure. Names and shapes of pieces, colors of squares, whether the "squares" are in fact square, even the physical existence of board and pieces, are all irrelevant. What is relevant is the number and geometric arrangement of the "squares", the number of types of piece and the number of pieces of each type, the quantitative-geometric power of each piece, etc. Everything else is a visual aid or a fairy tale.

It has been said that geometry is the art of applying good reasoning to bad diagrams.

She doesn't know geometry. Just enough to pilot a ship in and out of the folds." "Only that much?" I should have stuck to advanced finger-painting and never let Dad lure me into trying for an education. There isn't any end—the more you learn, the more you need to learn.

It is awkward to think that bacilli and other small organisms did not exist until we invented microscopes to see them, or that other galaxies did not exist until, in the 1920s, we invented telescopes powerful enough to detect them. Similarly, the past does not exist any longer for us, in ordinary perception, but it exists — and so does the future — in the geometry of Minkowski's space-time continuum.

The interwoven spheres and vines ran along the bottom. I'd done some research, and I'd found this motif everywhere. These overlapping circles were ancient, tracing back to Pythagorean geometry--geometry, a measure of the world. In more mystical terms, the shape had always evoked tghe place where world overlap: dreaming with waking, death with life, the visible with the unseen. [p. 362]

Logic was to cognition as geometry was to landscape

A square object was visible at a greater distance than a round object of the same area.