Quotes About Geometry

There are gaps in my education which no one could ever fill. But, they don't matter to me. I do not need to know science or algebra or geometry. Literature and music, painting and history-these are my passions. These are things that still, somehow in hours of quiet and lonesomeness, keep me alive.

Yep, I have to admit that isosceles triangles make me feel hormonal.

Human knowledge is dark and uncertain philosophy is dark, astrology is dark, and geometry is dark.

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.

Geometry is 'number in space', music is 'number in time'.

Islamic patterns speak of infinity and the omnipresent center.

Ludwig Schlafi (1814-1895) proved that there are six regular four-dimensional polytopes (generalisations of polyhedra): the 5-cell made of tetrahedra, the 8-cell or tesseract made of cubes, the 16-cell made of tetrahedra, the 24-cell made of octahedra, the 120-cell made of dodecahedra, and the 600-cell made of tetrahedra.

The rhombic dodecahedron is a three-dimensional shadow of the four-dimensional tesseract analogous to the hexagon as a two-dimensional shadow of the cube.

Schlafi also proved that in five or more dimensions the only regular polytopes are the simplex, or generalized tetrahedron, the hypercube, or generalized cube, and the orthoplex, or generalized octahedron.

Many familiar objects from cassettes to credit cards and Georgian front doors are Phi (1.618...) rectangles.

When one circle is drawn over another like this so that they pass through each others' centers, then an important almond shape, the vesica piscis, literally 'fish's bladder' is formed. It is one of the first things that circles can do. Christ is often depicted inside a vesica.

The dodecagon is also made from six squares and six equilateral triangles fitted around a hexagon

Twelve is the number which fits around one in three dimensions in the same way that six fits around one in two dimensions. The New Testament is a story of a teacher surrounded by twelve disciples.

Ten is formed from two pentagons and ten life-invoking pentagons sit perfectly arpund a decagon, and DNA, appropriately as the key to the reproduction of life, has ten steps for each turn of its double helix, so appears in cross-section as a tenfold rosette.

Eleven is important as the first number that allows us to begin to comprehend the measure of a circle. This is because, for practical purposes, a circle measuring seven across will measure eleven halfway around.

God is always doing geometry. —Saying attributed to Plato

Descartes's worldview makes us spiders at the center of an enormous web not of our making. Or in his other famous formulation, we are the ghosts in the machine: souls in a world machine that operates inexorably and impersonally according to the laws of geometry and mechanics, while we operate the levers and spin the dials.

The universe, Galileo wrote, "is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures, without which it is humanly impossible to understand a single world of it." Without mathematics, he concluded, "one wanders about in a dark labyrinth"—or what Plato might have called a cave.

In truth, a good master mason could build an entire Gothic cathedral with just a compass and a T square, a device he borrowed from Greek mathematicians for lining up perfect vertical and horizontal lines. This dazzling command of practical geometry made the cathedral builders of the Middle Ages truly independent businessmen. By the fourteenth century, they were already calling themselves free masons.

This was all the average Platonist needed to hear. He didn't care about "saving the appearances," as Aristotelians did—that is, making sure that everything we see and perceive has some explanation in our general theory. The Platonist knows appearances can deceive, because matter changes. Soccer balls come and go; they get run over or get stolen. However, the geometry describing their behavior, whether spinning on their axis or at rest, lasts forever.

It was the math that mattered. And when the math yields a pattern of harmonious proportion, whether it's the golden section of the Greeks or the Sierpinski gasket and Mandelbrot set of modern fractal geometry, the Platonist knows, as Archimedes did many centuries before, that he is standing at the threshold of the truth.

A superfície não crê no cubo ou na esfera.

Of the two alternatives - a curved manifold in a Euclidean space of ten dimensions or a manifold with non-Euclidean geometry and no extra dimensions - which is right? I would rather not attempt a direct answer, because I fear I should get lost in a fog of metaphysics. But I may say at once that I do not take the ten dimensions seriously; whereas I take the non-Euclidean geometry of the world very seriously, and I do not regard it as a thing which needs explaining away.

In this dynamic rivalry between house and universe, we are far removed from any reference to simple geometrical forms. A house that has been experienced is not an inert box. Inhabited space transcends geometrical space.