Axioms In Geometry Quotes & Sayings

It is well known that geometry presupposes not only the concept of space but also the first fundamental notions for constructions in space as given in advance. It only gives nominal definitions for them, while the essential means of determining them appear in the form of axioms. The relationship of these presumptions is left in the dark; one sees neither whether and in how far their connection is necessary, nor a priori whether it is possible. From Euclid to Legendre, to name the most renowned of modern writers on geometry, this darkness has been lifted neither by the mathematicians nor the philosophers who have laboured upon it. — Bernhard Riemann

The full impact of the Lobachevskian method of challenging axioms has probably yet to be felt. It is no exaggeration to call Lobachevsky the Copernicus of Geometry [as did Clifford], for geometry is only a part of the vaster domain which he renovated; it might even be just to designate him as a Copernicus of all thought. — Eric Temple Bell

Have a definite opinion. — William Safire

The truth is, when I got started in this business, it wasn't because I had a full understanding of the importance of the business, but because I thought it was fun. I found it exciting. It fulfilled me, whatever it was that I was looking for. — Sam Donaldson

By refraining from reducing multiplication to addition we are enabled through these axioms to banish continuity, which is so difficult to fix precisely, from the logical structure of geometry. — Hermann Weyl

If we must die, then let us die fighting a battle worthy of remembrance in the tales of our descendants! — Daniel Adorno

As an artist you look into yourself to understand the human potential to be all kinds of things that are not necessarily pleasant but are real - a criminal, a murderer, a sadist, a rapist; to be all of these things that many people are. You can't allow yourself to say, 'I'm a different species from those people.' Because you aren't.
The criminal as monster is kind of common. That's very convenient because you can then say, 'Of course I'm not a monster, therefore I'm not a criminal therefore I have no potential in tern of criminality.' And that lets you off the hook. That gives you a nice wall between yourself and them. — David Cronenberg

A man never rises higher than when he does not know whither his path can still lead him. — Oliver Cromwell

Boarding-House Geometry DEFINITIONS AND AXIOMS All boarding-houses are the same boarding-house. Boarders in the same boarding-house and on the same flat are equal to one another. A single room is that which has no parts and no magnitude. The landlady of a boarding-house is a — Stephen Leacock

Geometry, like arithmetic, requires for its logical development only a small number of simple, fundamental principles. These fundamental principles are called the axioms of geometry. — David Hilbert

Do you remember, Meir, that epigram quoted in the name of Rabbi Johanan ben Zaccai: 'There is no truth unless there be a faith on which it may rest'? Ironically enough the only sure principle I have achieved is this which I have known almost all my life. And it is so. For all truths rest ultimately on some act of faith, geometry on axioms, the sciences on the assumptions of the objective existence and orderliness of the world of nature. In every realm one must lay down postulates or he shall have nothing at all. So with morality and religion. Faith and reason are not antagonists. On the contrary, salvation is through the commingling of the two, the former to establish first premises, the latter to purify them of confusion and to draw the fullness of their implications. It is not certainty which one acquires so, only plausibility, but that is the best we can hope for. — Milton Steinberg

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. — David Berlinski

The only time you seem honest is when you're insulting someone!"
"The only honest things I can say to you are insults. — Brandon Sanderson

The Tartar looked at the sky. The stars were as many as at home, there was the same blackness around, but something was missing. At home, in Simbirsk province, the stars were not like that at all, nor was the sky. — Anton Chekhov

You might ask why we cannot teach physics by just giving the basic laws on page one and then showing how they work in all possible circumstances, as we do in Euclidean geometry, where we state the axioms and then make all sorts of deductions. (So, — Richard Feynman

Since these words went into William's fermenting little brain not as word memories, but as circuitry for storing word memories, bricks used to build the kiln for firing bricks, he has no recollection of the rhyme, yet the ideas in it are axioms of his mental geometry. — Dennis Vickers

What both the state and the capitalist economy oppose is an understanding of what might be called "the true nature of things" (using the phrase without metaphysical pretensions), especially injustices and exploitative practices. — Richard A. Falk

I've auditioned for normal characters. But I never get cast. — Jared Harris

Don't give me truth, just give me gossip
And skeletons from people's closets,
I wanna be normal
And millions buy it,
I am blinded by The SUN. — Benjamin Zephaniah