Quotes About Euclidean

It was built in 1912 and rebuilt in 1934, and offers, as do most Boston artifacts, a compromise between Man's Euclidean determinations and Nature's beguiling irregularities.

Another example of a class of well-defined mathematical problems that have no algorithmic solution is the tiling problem. This is formulated as follows: given a set of polygonal shapes, decide whether those shapes will tile the plane; that is, is it possible to cover the entire Euclidean plane using only these particular shapes, without gaps or overlaps?

result: every description of events in space involves the use of a rigid body to which such events have to be referred. The resulting relationship takes for granted that the laws of Euclidean geometry hold for 'distances', the 'distance' being represented physically by means of the convention of two marks on a rigid body.

In gravitational fields there are no such thing as rigid bodies with Euclidean properties; thus the fictitious rigid body of reference is of no avail in the general theory of relativity. ... For this reason non-rigid reference-bodies are used, which are, as a whole, not only moving in any way whatsoever, but which also suffer alterations in form ad lib. during their motion... This non-rigid reference-body, ... might appropriately be termed a reference mollusc,...

We thus obtain the following result: every description of events in space involves the use of a rigid body to which such events have to be referred. The resulting relationship takes for granted that the laws of Euclidean geometry hold for 'distances', the 'distance' being represented physically by means of the convention of two marks on a rigid body.

In gravitational fields there are no such things as rigid bodies with Euclidean properties; thus the fictitious rigid body of reference is of no avail in general relativity.

I see now the virtue in madness, for this country knows no law nor any boundary. I pity the poor shades confined to the Euclidean prison that is sanity

Not that the propositions of geometry are only approximately true, but that they remain absolutely true in regard to that Euclidean space which has been so long regarded as being the physical space of our experience.

My family was well off but not rich. I spent the four years I was an undergraduate working on the beach. And it wasn't because I was lazy; it was because my freshman class would go to a hundred different employers and wouldn't get a nibble. That was a disequilibrium system. I realized that the ordinary old-fashioned Euclidean geometry didn't apply.

The proof of Euclidean geometry's consistency eluded mathematicians. By the end of the nineteenth century, the best that was achieved was a proof that Euclidean geometry was consistent as long as arithmetic was consistent.

By the end of the nineteenth century, the best that was achieved was a proof that Euclidean geometry was consistent as long as arithmetic was consistent.

SINCE EUCLIDEAN MEASUREMENTS—length, depth, thickness—failed to capture the essence of irregular shapes, Mandelbrot turned to a different idea, the idea of dimension. Dimension is a quality with a much richer life for scientists than for non-scientists.

This is still the legacy of Euclidean geometry, where space has three dimensions, a plane has two, a line has one, and a point has zero.

No very good sense can be given to the idea that the elements of Euclidean geometry may be found in nature because either everything is found in nature or nothing is. Euclidean geometry is a theory, and the elements of a theory may be interpreted only in terms demanded by the theory itself. Euclid's axioms are satisfied in the Euclidean plane. Nature has nothing to do with it.

every possible Euclidean and non-Euclidean permutation of lights; ten thousand lights, ten million lights, the ten billion lights of Great Yu, each one a voice calling, "I is what I am! Notice me! Notice me!

Nature deals in non-uniform shapes and rough edges. Take the human form. There is a certain symmetry about it, but it is, and has always been, indescribable in terms of Euclidean geometry.

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.